Yes, which is precisely the problem: No one would need to be "convinced" of God when standing in His presence. That would eliminate choice and free will; do you "believe" or "have faith" in the screen on which you read this, or do you know it to be real? Outside a temporal reference frame to enable it, decision making in general gets tricky and, setting aside "eternity," non-material temporality is even more problematic (one reason literalist approaches to Eden are too restrictive; how long is a year in a static universe?) Ignorance may not be bliss, but temporary ignorance enables free will, and the story of the Fall seems to me more about that than about anything else.

That brings us to the sad state of Eve you referenced above (as well as the sad state of Adam about which you seem fairly impassive. ) Interesting stuff in that passage. For one thing, looking carefully reveals God does not give Adam command of Eve, only states that her desire for him will prompt her to submit to him, a phenomenon real enough for feminist scholars to spend decades railing against their weak willed sisters. God also incidentally tells Adam he and all his descendants will DIE for his sin, and have to work for a living. But before all that He says something else to the serpent:

Now, unless one thinks whoever the biblical author genuinely thought all reptiles were ought to get man from the start, the serpent of Genesis must be understood as a greater malevolent entity, either in the form of a serpent or taking control of one. That means the biblical author does not mean God declared an interspecies war, but instead promised one of Eves descendants would suffer greatly at the hands of that evil entity yet thereby win a final victory over him.

Every single descendant of Eve, whom the bible claims was mother of us all, would be heir to that promise. Some might forget it in whole or in part, and obviously THEIR descendants would never hear of it, but that would neither negate nor revoke the promise. Further, man had and has more than merely the words in a single tribes book to beat witness of God (though that same book later claims God literally created the Hebrew race from a single old man to preserve His covenant, precisely because everyone else forsook Him.) While sin must be a barrier to any perfect being (because tolerating sins presence would unmake any being DEFINED as perfect,) God need not and would not ignore man nor cease entreating reconciliation. It seems obvious no loving father would reject a repentant man who ignorantly but sincerely strives to love and serve his Maker.

The bible does not rely on merely being obviousness though; it explicitly states that:
In other words, the "righteous pagans" (to use the classical term) are not condemned for buying their genetic lottery ticket too early or in Botswana; they are held accountable for faith in the ancient promise apart from any missionary, on the basis of bare existence and the wonders of the universe as Gods witness. However, after 200,000 years or so, as we simultaneously (but surely coincidentally ) stand on the brink of full apostasy and a half dozen means of self annihilation, the promise is fulfilled, and there is a grave difference between partial ignorance of God and conscious rejection of Him.

Still and so, the choice remains the individuals; as in Pauls day, some will mock the whole notion of resurrection from the dead, and others will hear more from him. In the story of Lazarus (the only story Jesus told where a "character" had a name and Jesus did NOT explicitly call it a parable) the rich man begs Moses to send Lazarus to his brothers so they will repent, and Moses says they have the Law and the Prophets to teach them. The rich mean protests that he also had the Law and the Prophets but did not repent, but that if Lazarus returns from the dead his brothers will listen; Moses replies that if they did not believe the Law and the Prophets they will not believe even one risen from the dead. All things considered, it is difficult to say he was wrong.