You're operating under the connotative definition of "
chavvah," not the denotative definition. Denotatively the word means "breathe" or "live," not "life." In other words, the person who'd help bring death into the world was named "live," not "life." Even more fundamentally, Adam was naming her
his living person, not God's. As another poster has already pointed out, to name a person or thing is to assert a certain authority or dominion over that thing or person. Therefore, it may not be a good thing that ha'adam named le'issah "
live" or "
life," especially if he meant Eve to replace the tree of life. That act would then be considered an act of idolatry (piling on to the already implicit idolatrous act of choosing his will over God's when he disobeyed God. I think you're on more solid ground when focusing on the two having been (previously) made together (as another poster has asserted). Perhaps Eve did think Cain came from God (which is true) but thinking he might be a/the redeemer would be another act of idolatry. She'd have to think and believe he was the tree of life outside of the garden from which they'd just been banned for the express purpose of NOT partaking of the tree of life. She'd have to assume she could produce a tree of life herself (which would be yet another act of idolatry). There's another layer to this and that would be the premise the child came from God after she'd had sex, which is not the case with the incarnation. There's a lot of speculation growing in and from this premise Adam and Eve (one, the other, or both) believed they could produce redemptive life.
Since scripture itself is silent answering the question, the answer to this op's inquiry cannot escape speculation, but to what degree is that speculation reasonable and firmly rooted in a sound exegesis of scripture? That's what we should all be asking ourselves. Lot's of good stuff here,
@LeviR, but I think there is a better answer.