nothing in the text or the judgement indicates Adam did not believe. 1 Timothy 2:14 says he was not deceived. if he did not believe, or he was under the impression he would not die if he ate the fruit, then 1 Timothy 2:14 is contradicted.
Adam knew exactly what he was doing and what the consequences were. he knew if he did not eat, his wife would die without him. he knew if he did, he would die with her.
Romans specifically calls him a type of Christ, and Timothy is specific that he fully and accurately understood what was going on.
if he was in unbelief God would have judged him for it, don't you think? but God said 'because you listened to your wife' -- so Woman said something to him, and he, not deceived, listened to it.
she therefore didn't say something trying to trick him. she wasn't lying to him. she said something that he understood and made a fully informed, calculated decision about -- and then ((IMO)) he kept the two of them from eating from the tree of life, because he also understood that they shouldn't, until God arrived and sealed it off, preventing them from going back to it in the case that later as they continued to die, Adam either could not keep them from it or his mind decayed and he wasn't any longer able to keep himself from it.
it is important that the man and the woman whom death has entered do not eat from the tree of life in that state. but God "keeps" the way to it -- something has to happen first, before mankind can eat of it. we have to be cleansed, and that is what the Son of Man comes to do
"that we may have life"