I assert with confidence that,
1. God's omniscience allows Him to be the most free and most creative Being, omniscience in no way reduces His transcendence -- Does the LORD have freedom as the greatest creative Being? I ask because does God have to decide from eternity past all He wills to do in whatever future occurs? If God knows the future exhaustively, which would have to include His own future works, then He at one time might had more freedom and creativity than He does now. He must have, if He knows the future exhaustively. This is hard to square with an infinitely creative and free God. This is not theologically ok, because it puts God in a box He put Himself in, it's not biblical.
2. The working of God's omniscience is not fully known by us - Our current understandings of omniscience fail on both sides of the Arminianism and Calvinism divide, because we often imagine God as less than free or less than creative. Our whole understanding of God's omniscience fails if we put God in a box and by doing so malign His transcendence. His ways and thoughts are far beyond ours as the heavens are to the earth. However, God has still revealed much about Himself, about His attributes, in His Word. We are to reflect on these things. Thus, God is still known to us as far as He has so far revealed Himself to us. That said, we anthropomophize God by claiming to know how His mind works in relation to His judgments about the future, because God has not revealed much on how He understands the future in the bible.
3. God knows knows details about the future far in advance -- The mere scope of biblical prophecy reveals this. One cannot read Daniel 7-12, The Book of Revelation, or the Prophecies of the greater and lesser prophets in the Old Testament without realizing God knows the future in stunning detail. That said, again humility is called for here in refence to how God knows all this while respecting His creativity and freedom.
I am very interested in talking about any biblical verses that can show that God can change His mind, come to regret an action after the fact, or anything similar.
@Derf B You had much you had studied. I'm all ears.
4. God wants all men saved -- These scriptures go to proving this statement in both the Old and New Testaments. There is no soul God does not want to come to repentance.
Ezekiel 18:23 NASB
Do I have any pleasure in the death of the wicked,” declares the Lord God, “[k]rather than that he should turn from his ways and live?
Ezekiel 18:32 NASB
"For I have no pleasure in the death of anyone who dies," declares the Lord GOD. "Therefore, repent and live."
Ezekiel 33:11 NASB
"Say to them, 'As I live!' declares the Lord GOD, 'I take no pleasure in the death of the wicked, but rather that the wicked turn from his way and live. Turn back, turn back from your evil ways! Why then will you die, O house of Israel?'
Lamentations 3:33 NASB
For He does not afflict willingly
Or grieve the sons of men.
Matthew 23:37 NASB
37 “Jerusalem, Jerusalem, who kills the prophets and stones those who are sent to her! How often I wanted to gather your children together, the way a hen gathers her chicks under her wings, and you were unwilling.
1 Timothy 2:3-4 NASB
3 This is good and acceptable in the sight of God our Savior, 4 who desires all men to be saved and to come to the [c]knowledge of the truth.
2 Peter 3:9 NASB
9 The Lord is not slow about His promise, as some count slowness, but is patient toward you, not wishing for any to perish but for all to come to repentance.