I like your idea about Chavah, Eve being perhaps prepubescent when created.Scripture records the birth of very few individuals generally. Of Adam and Eve's children, only Cain (the first murderer), Abel (the first murdered man) and Seth (the descendent of Noah and therefore essential for all genealogies) are recorded. The first two because of a significant event, the last for genealogical purposes.
I try to avoid speculation, when there are old sources that don't disagree with scripture and are plausible I assume they are more likely to be correct than anything I come up with.According to Josephus, they already had daughters by the time of Abel's murder, Cain was already married at this time and took his wife when he left, they had more sons and daughters afterwards, and he cites an old Jewish tradition that in total they had 33 sons and 23 daughters (see footnote 8 in the link above) - ie far more than seven allowing us to interpret God's statement to Cain as meaning vengence on seven individuals. That all makes perfect sense with scripture, so I just assume it's probably about right.
Regarding the speed of reproduction, although they were perfectly fertile that doesn't necessarily mean a baby every single year. Firstly, Eve may have been created prior to puberty and only reached puberty later (and puberty may have been at an older age given the total lifespan was longer), which could explain a delay prior to Cain if such a delay did exist (which we don't know anyway). A fertile woman today will produce one child every 3-4 years if she exhibits lactational anoestrus (ie does not ovulate while producing milk) and breastfeeds for >2 years, or every 12-18 months if she does not exhibit lactational anoestrus. Lactational anoestrus is the "normal" condition for most mammals, for instance wild cattle exhibit lactational anoestrus and reproduce slowly, while farmers have bred this trait out of domestic cattle to allow them to get pregnant during lactation to have a calf every year. If we assume that a strong lactational anoestrus is the intended "perfect" condition, because it makes sense for a woman's body, and that this trait has been diluted in the current population as women who do not exhibit it produce more offspring and are therefore selected for, and that Eve would have breastfed for long periods due to the unavailability of processed food to wean children on to, Eve would have produced offspring at a much slower rate to that experienced in our own lives when we do not use birth control. This makes the number of 56 offspring sound about right (one every 8 years or so over a pre-menopausal window of 500 years or so). Now obviously I'm speculating a bit with these numbers, but not in order to invent my own ideas, simply to show that the numbers presented by Josephus are plausible biologically and we have no reason to think they are erroneous.
I sound like a cattle breeder, sorry ladies, when it comes to reproduction I start thinking in terms of cows and sheep...
It sure ties in nicely to the concept that they did not feel shame for being naked.
The only thing I'd mention and you probably know this is that in Genesis 2:23 we're told she's to be called "woman"
וַיֹּאמֶר֘ הָֽאָדָם֒ זֹ֣את הַפַּ֗עַם עֶ֚צֶם מֵֽעֲצָמַ֔י וּבָשָׂ֖ר מִבְּשָׂרִ֑י לְזֹאת֙ יִקָּרֵ֣א אִשָּׁ֔ה כִּ֥י מֵאִ֖ישׁ לֻֽקֳחָה־זֹּֽאת׃
"And the man said this time, substance from my (own) substance, and flesh from my flesh, for this (reason) she is called woman, because she was taken from man". The Hebrew word play; she's called "Ishah" because she's taken from "Ish". I messed with the English tense a bit because an imperfect verb can also be our present tense (just to make a point) so don't get up in arms with me people if it's different than most translations.
So the point is Ishah means woman, not female right?
Now this is not a strong point because the statement can be very general right like women are called women because they came from man so it doesn't really knock out your prepubescent idea; just thought it's worth mentioning.