Where did people who lived in Jesus's time go to when they died?

The Book of Romans address Sin very clearly, please look through the book of Romans so that you may gain more insight.

To address your question, let me take the following verses from the Romans 2:12-16

12 All who sin apart from the law will also perish apart from the law, and all who sin under the law will be judged by the law. 13 For it is not those who hear the law who are righteous in God’s sight, but it is those who obey the law who will be declared righteous. 14 (Indeed, when Gentiles, who do not have the law, do by nature things required by the law, they are a law for themselves, even though they do not have the law. 15 They show that the requirements of the law are written on their hearts, their consciences also bearing witness, and their thoughts sometimes accusing them and at other times even defending them.) 16 This will take place on the day when God judges people’s secrets through Jesus Christ, as my gospel declares.

In verse 14, it talks about gentile who didn't receive the law of Moses, I doubt if anyone who can 100% saying that have obey all according to the 10 Commandments, that they have done no sin.

Verse 13 first explained that, it is not that someone hears the law that he is righteous in God's eyes. But rather to those who obey the law, may God declare him to be righteous. Anyhow, God is the judge. A justice God.

During Jesus time however, the salvation has not yet complete. Yet, Jesus has been declaring the kingdom of God is near. The salvation is near, where people may find themselves righteous in God's eyes as they accept Jesus as their personal Savior and obey His teaching as a disciple. Two criteria in one obedience.

You believe Jesus, then you do what He says.

Verse 15, when the gentiles have not bound to the law of Moses. Then it talks about the heart of the gentiles, and indeed as human being, we have a sense of moral, anyhow from the beginning of time until the day when Jesus completed the Salvation, for them it's the same all along. That in their consciousness, they know what is right and wrong. And because of this, God may judge them according to their hearts. Not by the law of Moses.

And everyone who died in anytime from the beginning of time, until the second coming of Jesus Christ in the future. They are not in heaven or hell, but rather, all will be risen from the dead. That is the resurrection before the Final Judgement. Those who died can not change their course, but those who are living can still make their choice. To be righteous in God's eyes is what matters.

Glory to God for his wisdom, justice, grace and mercy. Amen.

You seem to be thinking that when Jesus became man on earth he somehow ceased to be God in Heaven. The way people were judged was precisely the same during Jesus life on earth as it was before and as it was after. When God the Son became a man he did not cease to be God in all His fullness at the same time. God is outside of time, so He is the same yesterday today and forever.

As a Christian of the Reformed Protestant persuasion, I do not think there is anything in the New Testament to suggest that Jesus, when on earth, was personally or individually in the business of judging the dead, either Jew or Gentile, or of escorting them either to heaven or to hell. We know that our eternal destination is decided at the point of death. The basis of judgment is on how we lived our lives. Daniel spoke of the Book of Life and so does Revelation, in which names are written.

Ecclesiastes 12:6-7 informs us that we must remember God “before the silver cord is severed, or the golden bowl is broken; before the pitcher is shattered at the spring, or the wheel broken at the well, and the dust returns to the ground it came from, and the spirit returns to God who gave it.”

Significantly, verse 14 says “God will bring every deed into judgment, including every hidden thing, whether it is good or evil.”

So it is God who does the judging. Just because the third person of the Triune Godhead was temporarily on earth does not infer that the Father and the Holy Spirit were incapacitated in any way!

However, Jesus did have something to say about the condition of the dead and WHERE the soul went while awaiting the resurrection and the judgment to come. It’s in Luke 16:19-31:

There was a rich man who was clothed in purple and fine linen and who feasted sumptuously every day. And at his gate was laid a poor man named Lazarus, covered with sores, who desired to be fed with what fell from the rich man’s table. Moreover, even the dogs came and licked his sores. The poor man died and was carried by the angels to Abraham’s side [or bosom]. The rich man also died and was buried, and in Hades, being in torment, he lifted up his eyes and saw Abraham far off and Lazarus at his side. And he called out, ‘Father Abraham, have mercy on me, and send Lazarus to dip the end of his finger in water and cool my tongue, for I am in anguish in this flame.’ But Abraham said, ‘Child, remember that you in your lifetime received your good things, and Lazarus in like manner bad things; but now he is comforted here, and you are in anguish. And besides all this, between us and you a great chasm has been fixed, in order that those who would pass from here to you may not be able, and none may cross from there to us.’ And he said, ‘Then I beg you, father, to send him to my father’s house—for I have five brothers—so that he may warn them, lest they also come into this place of torment.’ But Abraham said, ‘They have Moses and the Prophets; let them hear them.’ And he said, ‘No, father Abraham, but if someone goes to them from the dead, they will repent.’ He said to him, ‘If they do not hear Moses and the Prophets, neither will they be convinced if someone should rise from the dead.’ (English Standard Version)

The Greek word ‘kolpos’ is variously translated as “Abraham’s side” (NIV, ESV), “next to Abraham” (CEV), “with Abraham” (NLT), “the arms of Abraham” (NCV) and “Abraham’s bosom” (KJV).

“Abraham’s bosom” was used in the Talmud as a synonym for heaven. The image in the story is of Lazarus reclining at a table leaning on Abraham’s breast at the heavenly banquet. The point of the story is that wicked men will see the righteous in a happy state, while they themselves are in torment, and that a “great gulf” that can never be spanned exists between them (Luke 16:26). Until the resurrection, the souls of those who have died are in an “interim holding place” – either in a state of bliss (paradise, or Abraham’s bosom) or in a state of torment.

It was at the cross that God pronounced judgment on the unbelieving world and on the enemy of our souls, Satan. Jesus said, shortly before His arrest, “Now is the time for judgment on this world; now the prince of this world will be driven out” (John 12:31). However, there are future judgments to come:

The judgments of the tribulation period (Revelation 6—16)

The judgment seat of Christ (2 Corinthians 5:10)

The judgment of the nations (Matthew 25:31–46) The judgment of angels (1 Corinthians 6:2–3)

The Great White Throne Judgment (Revelation 20:11–15)

This final judgment of unbelievers occurs at the end of the Millennium, before the creation of the new heaven and earth. At this judgment, unbelievers from all the ages are judged for their sins and consigned to the lake of fire (the permanent condition of those who reject Christ).

So, who judged all those persons who died while Jesus was on earth? The Bible does not say, and I’m not about to guess. It’s an interesting question but I suspect that the Father and the Holy Spirit had everything under their control (including sustaining the universe and all life) while the Logos, the Word of God, was on assignment for those few, short years when he dwelt with us.