The tree is used as a prophetic metaphor of the cross.
De 21:23 His body shall not remain all night upon the tree, but thou
shalt in any wise bury him that day; (for he that is hanged is
accursed of God;) that thy land be not defiled, which the LORD thy God
giveth thee for an inheritance.
Ga 3:13 Christ hath redeemed us from the curse of the law, being made
a curse for us: for it is written, Cursed [is] every one that hangeth
on a tree:
Notice how the law contains a shadow of the good thing coming? (Heb 10.1) This is sensus plenior.
The tree... the cross is life or death depending upon how you approach it, in grace or in judgement:
1Co 1:18 For the preaching of the cross is to them that perish
foolishness; but unto us which are saved it is the power of God.
The tree of life is the cross.
Since there are none righteous...
Ro 3:10 As it is written, There is none righteous, no, not one:
The righteous referred to must be Christ.
Pr 11:30 ¶ The fruit of the righteous [is] a tree of life; and he that winneth souls [is] wise.
Therefore: The fruit of Christ is the cross, the ultimate symbol of God's love. The verse has a shadow of the good thing coming.
The tree of life and the tree of 'death' (knowledge of good and evil) though literally two trees, are figuratively two aspects of one tree representing Christ. Christ, the same tree in Revelation is one tree with two roots, grace and law (holiness). Christ is the source of life or death depending upon how you approach him. The same of the water which gives life of floods to destroy, and the fire which destroys or refines. Christ reconciles law and grace as the one tree revealing both natures of God.
The cause of God's anger toward man is defined in Rom 1:18 ff, that he did not acknowledge God nor give him thanks. Though Adam walked with God, he considered him a peer, and he usurped God's position, making himself to be a God, by ignoring God's definition of good and evil by His very character, and instead determined that it was acceptable for him to eat the fruit. Once man had usurped the position of God by defining good and evil for himself 'knowing (or declaring) his own good and evil', Christ had to die on the cross.
Had salvation been given freely without the cross, God's holiness would not be manifest. As such, the Gospel was hidden until the time of Christ. This is the same reason that Jesus spoke in riddles and parables.
Mt 13:15 For this people’s heart is waxed gross, and their ears are
dull of hearing, and their eyes they have closed; lest at any time
they should see with their eyes, and hear with their ears, and should
understand with their heart, and should be converted, and I should
Mk 4:12 That seeing they may see, and not perceive; and hearing they may
hear, and not understand; lest at any time they should be converted,
and their sins should be forgiven them.
These passages indicate that Jesus did not want them to get saved at that time. They could not take of the tree of life until after the cross.