The “great deep”, תְה֑וֹם (te-home) t’hom – is not “earth’s core”, it is the waters that filled the primeval universe; it is a Hebraicized form of “Tiamat”, the chaos-monster. It is both above and below the heavens, pushed up from the earth-disk by the solid dome firmament and kept below the earth because the earth was raised by pillars that kept it from being inundated.
If you want to connect it to science, do what some ancient scholars did before the invention of the telescope (to put it in perspective): they concluded that the universe started out as the smallest thing possible and expanded rapidly beyond comprehension, filled with fluid that was too dense for light to propagate, and when it thinned enough by spreading out as the universe grew then God commanded light to shine. [note that these scholars just described the opening period of the Big Bang.
No – the t’hom, the great deep, was endless and had no surface apart from the action of the Spirit of God meditating over it; it was water all through (or fluid, if you want to go with those ancient scholars).
No cooling; the earth-disk came cool and dry when YHWH_Elohim pushed the waters off to the side and upwards.
No – the waters “above the heavens”, i.e. what the Genesis writer calls “waters above the expanse” were there before the earth-disk was since they were part of the t’hom, the great deep.
That call the writer a liar – it is directly contrary to the text.
You can make up all the science fiction you want, but don’t pretend it has anything to do with Genesis since you are ignoring the original worldview, ignoring the meanings of words, and ignoring plain statements of the text. What you are doing is not theology because it is not exegesis, it is made-up “ooh – shiny!” thinking that arises from not understanding what you’re talking about yet trying to fit it to something to which it has no relation.
I showed you two and referenced two others. I’ll try again:

Those are both ancient Egyptian drawings, both from the eleventh or tenth century B.C.
Watch this from about 11:00 to around 20:00; he covers Egyptian and Israelite views–
