Why did God create us so that it is in our nature to sin?

The key piece of the puzzle you are missing is love. To quote you above:

God has perfect free will but He will never sin because it is not in His nature.

Why? Because God's very nature is self-sacrificing love.

Now why can't God create sinless creations with a nature incapable of sining? Because love is from God.

Beloved, let us love one another: for love is of God; and every one that loveth is born of God, and knoweth God. 1 John 4:7

To quote the prominent Protestant writer Ellen White:

God's wonderful purpose of grace, the mystery of redeeming love, is the theme into which "angels desire to look," and it will be their study throughout endless ages. Both the redeemed and the unfallen beings will find in the cross of Christ their science and their song. It will be seen that the glory shining in the face of Jesus is the glory of self-sacrificing love. In the light from Calvary it will be seen that the law of self-renouncing love is the law of life for earth and heaven; that the love which "seeketh not her own" has its source in the heart of God; (The Desire of Ages, Pg 19)

So in the heavenly courts, in His ministry for all created beings: through the beloved Son, the Father's life flows out to all; through the Son it returns, in praise and joyous service, a tide of love, to the great Source of all. And thus through Christ the circuit of beneficence is complete, representing the character of the great Giver, the law of life. (Desire of Ages, Pg 21)

Creations were made to receive God's self-renouncing love and to reflect it back to Him through praises and willful service. If God creates creations who are self-sustaining embodiments of love themselves, well, then God would have created Himself.

God is love. 1 John 4:8

Did God "create us so that it is in our nature to sin"? After God had created Adam and Eve He "saw all tht he had made, and it was very good" (Genesis 1:31).

That means everything that God had created was without blemish, without fault, without sin. There was no "sin nature" in Adam or in Eve. Sin did not exist - up till the moment they decided to disobey God. Genesis chapter describes how, by that one action of disobedience, sin entered into their nature. They were immediately stricken with a sense of shame and unfitness, and they hid from God’s presence.

When they had children, Adam’s image and likeness was passed along to his offspring: "When Adam had lived 130 years, he fathered a son in his own likeness, after his image, and named him Seth" (Genesis 5:3). The sin nature manifested itself early in the genealogy: the very first child born to Adam and Eve, Cain, became the very first murderer (Genesis 4:8).

“Sin entered the world through one man, and death through sin, and in this way death came to all people, because all sinned” (Romans 5:14).

I may have misunderstood your question, but based on what the Bible says I reject the premise that God created Adam with a nature to sin. Adam was created perfect and without sin.

Edit for clarification: I found an article on what being created in the image of God means. A full explanation can be read (link provided), but this is a partial quote that seems relevant:

"Part of being made in God’s image is that Adam had the capacity to make free choices. Although they were given a righteous nature, Adam and Eve made an evil choice to rebel against their Creator. In so doing, they marred the image of God within themselves, and passed that damaged likeness on to all of their descendants (Romans 5:12). Today, we still bear the image of God (James 3:9), but we also bear the scars of sin. Mentally, morally, socially, and physically, we show the effects of sin."

Source: https://www.gotquestions.org/image-of-God.html

Have you ever tried to compare the differences between God’s nature and man’s nature? God is The Divine Being we are human beings. God’s being is Holy – thrice ‘holy’ (Isaiah 6:3) which is never stressed with his other attributes. That’s the starting point – the supreme holiness of God which us sinful human beings cannot begin to comprehend while we are tarnished with our sin. Don’t forget – WE sin. This isn’t a theological exercise about someone called Adam – it’s about the awesome Being of the Holy God who tells us what’s wrong with us, and how, through Christ, the last Adam, he lovingly enables that corrupt nature of ours to be restored to what it originally was created as: perfect and sinless. We can’t accomplish that as we are fallen and degraded by our sin. We should not tell God what our objections are to what he’s communicated to us already regarding that dilemma; we have to listen to him, then repentantly obey.

“For my thoughts are not your thoughts, neither are your ways my ways, saith the Lord. For as the heavens are higher than the earth, so are my ways higher than your ways, and my thoughts than your thoughts…. [My word] shall accomplish that which I please” (Isaiah 55:8-11).

Our sinful eyes can only be opened by God, should he graciously deign so to do. Attitude counts, and it is our attitude that is deficient, not Gods.

Our sin creates a huge chasm between us and our Maker, who remains untarnished. Adam fell into that chasm when he chose to follow his wife in a course of disobedience. She had been deceived; he had not. That is why the Bible says it was through the one man, Adam, that sin entered the world (Romans 5:14) The Q you raise is not about love or free will. It is about God’s holiness, his righteousness, and his justice yet this is the continuing flaw of sinful human beings – we actually try to justify ourselves before God. Yours is a good question which I’ve marked up, but only in order to expose the danger of this basic human flaw of pride if sinners use it to try to justify themselves. Please don’t take offense at me saying that. God declares,

“For thus saith the high and lofty One that inhabiteth eternity, whose name is Holy. I dwell in the high and holy place, with him also that is of a contrite and humble spirit, to revive the spirit of the humble, and to revive the heart of the contrite ones.” (Isaiah 57:15)

Persevere with the answer now the preamble is over.

Having re-directed the matter to the Being of God first, only after which we can understand the vexed matter of a sinful human being, please grasp the awesomeness of God’s Holiness, Righteousness, and Justice. For God to fail to exercise such attributes in perfect balance would be to fail to be the Almighty God. That would be to violate his own Being. Only he is God. We are not God. He declared to his covenant people,

“Before me there was no god formed, neither shall there be after me… I am the first, and I am the last; and beside me there is no God… Is there a God beside me? Yea, there is no God; I know not any… and I will not give my glory unto another.” (Verses from Isaiah chapters 43, 44 & 48)

Being created in God’s image and likeness gave man the ability to perfectly represent God on earth, to be his chosen agent for having the earth cultivated, to have its creatures in subjection and to procreate, all according to God’s perfect will. Man was created without sin tarnishing him or his divine commission. Man was not created unholy, unrighteous or unjust yet man was not created with God’s Being, for that belongs uniquely to the Creator. Man did, however, have available to him, eating from the Tree of Life, which necessitated avoiding eating from the Tree of the Knowledge of Good and Evil. To eat of the latter would be to deprive himself of eating of the former. A deceiver came along (a sinful creature outwith the realms of humanity) who ever so slightly twisted God’s words so as to cause the woman to fall for his trick, then the man chose to throw in his lot with her, rather than perhaps ‘lose’ her? Having received this fabulous companion, did he fear ending up on his own again? Back to what the scriptures actually tell us:

“The first man Adam was made a living soul; the last Adam was made a quickening spirit. Howbeit that was not first which is spiritual, but that which is natural; and afterwards that which is spiritual. The first man is of the earth, earthy; the second man is the Lord from heaven. As is the earthy, such are they also that are earthy; and as is the heavenly, such are they also that are heavenly. And as we have borne the image of the earthy, we shall also bear the image of the heavenly.” (1 Corinthians 15:45-49)

The Greek word ‘anthropos’ is used here to distinguish between a particular man and humanity. Humanity is made from the dust of the ground – we are ‘earthy’ (created from matter). The Word from heaven (spirit, not created matter) added human nature to his divine nature in order to be God’s means of delivering us from corrupted human nature inherited from the first ‘earthy’ man. The man, Jesus, imparts life eternal to those who will accept him as the gift God gave. The gift was the person of the Son of God. In that way the Son of Man offered up his body, his humanity, to redeem matters righteously, according to God’s perfect law of justice. Redemption wrought is righteousness wrought, then comes restitution to those accepting the gift.

Yet humanity that treats humanity as the purpose of its own existence, as if humanity can independently realise its own fulfilment by its own expression of itself and promoting its own views will never see what humanity is, from God’s viewpoint, and thus will continue to question the right of God to work matters out as he has chosen so to do. For God’s ways prove his utter holiness, righteousness and justice. And his love is supremely demonstrated in giving the Word, who is God, as his undeserved gift to fallen humanity, to redeem them from the pit. Who can see it? Who can grasp by faith, the rope that lifts us out of our pit, while the many keep seeking their own systems and theologies to contribute towards our redemption? God says we cannot even redeem ourselves, let alone another (Psalm 49:7-9 yet God will redeem David’s soul from the power of the grave; God shall receive him.)

Eden cannot be viewed clearly without standing at Golgotha, to see how

“Surely God’s salvation is nigh them that fear him; that glory may dwell in our land. Mercy and truth are met together; righteousness and peace have kissed” (Psalm 87:9-10).

To stand in Eden, pondering what happened there without taking God’s revelation of his salvation at Golgotha into consideration is an exercise in futility. Thus I have given the Bigger Picture, sola scriptura as requested, for your consideration. Consider what God has said and revealed, then your understanding will be changed, and for God’s glory.

1) Mankind was created at a certain point in time. (Genesis 1, 2)

2) God is eternal. (Genesis 21:33)

3) God cannot create an eternal being whose existence has a beginning that comes later than eternity past - that is a logical impossibility.

4) From this we can conclude that in at least some respects, God and humans are different. God has attributes (like eternal existence) that are not communicable to his creations.

5) God created man in his own image:

Genesis 1:26 Then God said, “Let us make mankind in our image, in our likeness, so that they may rule over the fish in the sea and the birds in the sky, over the livestock and all the wild animals, and over all the creatures that move along the ground.”

6) Therefore we can conclude there are attributes that God can and did communicate to his creations.

7) At least one aspect of that image is defined: man is granted a sphere of dominion over nature.

8) Not all respects in which man is in God's image are enumerated. Psalm 8:

4 What is man, that thou art mindful of him? and the son of man, that thou visitest him?

5 For thou hast made him a little lower than the angels, and hast crowned him with glory and honour.

6 Thou madest him to have dominion over the works of thy hands; thou hast put all things under his feet.

9) The Bible addresses the question of why we were constructed (individually or collectively) in one way and not another. Isaiah 45:9 says:

9 “Woe to the one who argues with his Maker— one clay pot among many. Does clay say to the one forming it, ‘What are you making?’ Or does your work say, ‘He has no hands’?

10) The evidence from Genesis 3 is that regardless of the nature Adam and Eve had prior to the fall, their nature changed, and we inherit that nature just as surely as we inherit our parents' DNA.

11) The change in nature was Adam and Eve's fault as punishment for their sin, an act of judgment by God. The full scope of the change is not described, but aspects of it are given in Genesis: knowledge of good an evil, pain in childbirth, troubled relationships between men and women, and physical death.

12) This leaves the main question. Since the fall, it is in our nature to sin, as described by Paul in Romans, especially chapters 3 and 7. Before the Fall, mankind was neither incapable of sin nor prone to sin: Adam and Eve were innocent. Differnt from God (who cannot) sin, but also different from us (who have a sin nature). Thus God did not originally create us with a nature prone to sin.

The OP asks for a non-speculative answer, but the OP is asking a speculative question regarding what might have happened to humanity had Eve not done as she did and had Adam not done as he did.

However I am answering this from a Protestant and Christian perspective, for both of those I am.

The fact is that what God created was good. And the fact is that the (created) Serpent did what he did, the (created) woman did what she did and the (created) man did what he did.

That which was created conspired against the Creator. And this was the the best creation that could ever be created !

Did Deity create less than the best ? Let it not be !

The fact is that there is an inherent liability in creation itself. The very existence of a creation at all causes something to be there. It springs into existence by the very act of creation.

The tree of the knowledge of good and evil. And God immediately warned Adam of that which was there and warned Adam of the consequences of it.

It is because of that that the Serpent did as he did, that Eve did what she did and that Adam acted the way he did.

This is what created beings did. This is what created beings will always do. It's how created beings behave !

But Deity already knew of this. And from before the foundation of the world, Ephesians 1:4, was there a unanimous agreement. And from the foundation of the world, there was a sacrifice in view :

The Lamb slain from the foundation of the world. Revelation 13:8.

Great is the wondrous salvation of God Almighty who, in his wisdom, foresaw all things, yet in love refrained not from his ultimate purpose :

in bringing many sons to glory, Hebrews 2:10.

Creation was but a necessary precursor to the ultimate purpose of Almighty God who desired to share his existence with sons whom he would father.