hmmm
well although i dont know the answers to your question, and i kinda think no one does, i do know why it looks so weird to us to imagine lack of space or time, or as you said, fucks with our minds
we are used to stuff being at least somewhat intuitive as most of the laws of nature we evolved under, are visible to us. for example i didnt need newton to tell me that an apple will fall to the ground, i knew that. i might not have had the exact formula for it, but i understood it well intuitively. but once relativity and quantum mechanics came, we couldnt understand shit intuitively anymore, as we didnt have any experience with things that were big/fast/small enough to qualify. i know that relativity states that if i go at the speed of light, time stops for me. i know from quantum mechanics that that entangled particles can send information back in time. nothing of it makes any intuitive sense at all
so i assume a lot of things are possible that dont make sense as we dont have experience with it
as for the space question, im not really sure what to think
big bang may have started both space and time. oor the big bang was just one in an infinite space (inflation theory). actually i remember roger penrose talking about it in some jordan peterson podcast. i dislike jordan peterson so i had trouble following it, but i think penrose said how we could detect gravitational waves from before the big bang (other universes i assume), which would i guess mean big bang just happened in space and didnt make it, but im too lazy and sleepy to even try to understand that fucking autist penrose at this time
also every time i heard anything about gravitational waves, it turned out to be a nothingburger
my general approach is, if something is counterintuitive, im not even gonna bother with trying to understand it. and that goes for relativity and quantum mechanics as well as more mundane things such as fiat economy and girls with daddy issues