Since the term "predestination" in your question specifically refers to God's choice of individuals for blessed eternal life or eternal damnation, after death, and with that understanding, I would like to make short comments:
First, is it knowable? The answer is a "binary" one: if you are "in" then you are "not
out." And the best place to find the answer in the Scripture:
Jesus says,
- "My sheep hear my voice, and I know them and they follow me (Jn 10:27).
- "And I have other sheep(you and I) that are not of this fold. I must bring them also, and they will listen to my voice (v 16);
- "When he has brought out all his own, he goes before them, and the sheep follow him, for they know his voice. A stranger they will not follow, but they will flee from him, for they do not know the voice of strangers.” (v4-5).
- "Truly, truly, I say to you, unless one is born of water and the Spirit, he cannot enter the kingdom of God. That which is born of the flesh is flesh, and that which is born of the Spirit is spirit. ....The wind blows where it wishes, and you hear its sound, but you do not know where it comes from or where it goes. So it is with everyone who is born of the Spirit.”
So, it is knowable, and the knowing is between you and the Lord, a personal thing. And NO denomination or any human can claim to know for certain.
The Holy Spirit says,
- Romans 8:16 -"The Spirit himself bears witness with our spirit that we are children of God."
So, it is knowable and knowing comes from your inner person, because the Holy Spirit abides in you as "Parakletos" (Πνεύματος), and works within you. Paul says, "can you NOT know when He is in you? (Paul uses an analogy of being drunk with wine (Eph. 5:18.)
- Scripture witnesses that, where ever He, the Holy Spirit appears, i.e, Gen. 1:2, a new order and creation happens, and changes occur. When believers in faith yield to Him, they will see He "bear witness"- slow but radical changes in your prayer, devotion, and attitude to others Because, your world view changes, so the value system, and purpose of life, etc. You will become "seeking His kingdom and His righteousness first", etc. You will repent and confess your sin that is the sure way a child can enjoy the peace and love of God in your life.
More Texts to meditate:
- the Parables- the Pearl merchant & the treasure hunter (Mt.13:44, 45-46).
- "Jesus says, "You are the light" implies the darkness will flee from you and in your presence, and "you the salt" - people associate with you will see what difference you bring into their life.
Conclusion
Yes, it is knowable, NO one else can claim to know for sure, but you and people around you will notice something going on with you, and the Lord knows YOU are His, that's all that matter. Blessings to you!
PS: I have a comment might you find interesting: "what is the role of our will" the link:{here}