was it that singularity?
yes.
what makes us so sure?
it's generally accepted...but no one is sure...maybe, for example, time is eternal...
big bang is a favorite, little bang also a possibility...Strictly speaking, the big bang model has very little to say about the big bang itself. It describes what happened afterward.
what does GR predict?
GR and QM breakdown at such singularities as big bang and black holes...useful but not a final conclusive answer. But GR posits that space and time are NOT fixed, they change and for some reason gravity is a consequence of mass, energy and pressure...says nothing about which came first.
Ultimately nobody knows what space and time are nor how they are related. Nor how they relate to matter and energy...all have "mysterious" unexplained origins...
You can read a lot of posts about spacetime on the forms here by searching Ted Jacobsen, Verlinde, Renate Loll, emergent spacetime, for a start...
please be as detailed as you can and take your time if you have good information even if there are any equations. thanks in advance !