But of the tree of the knowledge of good and evil, thou shalt not eat of it: for in the day that thou eatest thereof thou shalt surely die. [Genesis 2:17 KJV]
The only prohibitive command was not to eat of the tree of knowledge of good and evil.
Now the serpent was more subtil than any beast of the field which the LORD God had made. And he said unto the woman, Yea, hath God said, Ye shall not eat of every tree of the garden? [Genesis 3:1 KJV]
The serpent questioned the command. There was no need to answer the serpent but the correct answer would have been 'No, we are allowed to eat of every tree of the garden'. For the tree of knowledge of good and evil is not stated to be in the garden.
The question is deliberately confusing.
But of the fruit of the tree which is in the midst of the garden, God hath said, Ye shall not eat of it, neither shall ye touch it, lest ye die. [Genesis 3:3 KJV]
Eve confused the two trees. She thought the forbidden tree was in the midst. It was not. The tree of life was in the midst. The serpent did not correct her. He left her confused.
And when the woman saw that the tree was good for food, and that it was pleasant to the eyes, and a tree to be desired to make one wise, she took of the fruit thereof, and did eat, and gave also unto her husband with her; and he did eat. [Genesis 3:6 KJV]
The woman ate of the tree of knowledge of good and evil only. There is no record of she or her husband partaking of the tree of life.
And Jehovah God saith, `Lo, the man was as one of Us, as to the knowledge of good and evil; and now, lest he send forth his hand, and have taken also of the tree of life, and eaten, and lived to the age,' [Genesis 3:22 Young's Literal Translation]
Young's Literal Translation indicates that now, the man was no longer as God (in respect of the tree of knowledge of good and evil) so the man is banished lest he also reach out and take of the tree of life and live for ever.
Whether he can or not, whether he is willing to or not, whether he is of a mind to do so or not, is completely irrelevant.
He will not be permitted to do so.
He had, as yet, clearly not done so. He could have done so, but now, having first taken of the tree of knowledge of good and evil, he is not permitted to - as well - take of the tree of life. He has made his choice and he cannot change it.
Mankind, in Adam, will never partake of the tree of life. He will age and he will sweat for his food and he will die.
But a provision is made for these two individuals, personally. God makes a sacrifice on their account and clothes them with skins.
And Adam believes the promise (of a seed yet to come through woman) and Adam calls her 'the mother of all living'.
And Adam called his wife's name Eve; because she was the mother of all living. [Genesis 3:20 KJV]