The tree of life in Proverbs 3 is understanding and wisdom. The fruit of the tree of knowledge did not contain either, only knowledge. In order for man to obtain understanding and wisdom, he had to do that on his own via the gifts contained in the Image he was created in.
Notice the Cherubim stands only at the one edge of the Garden. He isn't standing guard to keep man out; he's guarding the path to the Garden to keep it open — open to the tree of life. Gen 3:24, "So He drove out the man; and He placed at the east of the garden of Eden the cherubim, and the flaming sword which turned every way, to keep the way to the tree of life." The fruit of the tree of life is understanding and wisdom.
Attaining understanding and wisdom requires choices to be made, as per the OODA loop.(see Boyd: observation, orientaiton, decision, action) God does not do one's thinking for them. Note Peter's exercise of the loop. John 6:68, "Simon Peter answered him, “Lord, to whom shall we go? You have the words of eternal life." Those words are understanding and wisdom. They are the fruit of the tree of life which is in Paradise and y'all were invited to eat, since y'all are what you eat. John 6:63, "The Spirit gives life; the flesh counts for nothing. The words I have spoken to you are Spirit and they are life." John 6:48, "I am the bread of life."
Is the ‘tree of life’ in Genesis and Proverbs and Revelation all the same ‘tree’? AND curious that the ‘tree of life’ and that ‘tree of the knowledge of good and evil’ already existed before Genesis 1:3, else we would have been told of their ‘creation’. God said up to then end of Genesis chapter 1 that what he created was GOOD, however after the end of Genesis 1 we do not see those words attributed to what follows.