When did the ablative originate? Additionally, I’d like to know which case was used before the ablative for adverbials. I think it replaced the dative, as I also study Ancient Greek. In that language, the dative is used.
The Latin ablative case represents a merger of three earlier Proto-Indo European (PIE) cases: the ablative (sometimes referred to as the 'from' case, because it was used to express ideas of source, separation, etc. – ideas where English often can use the preposition 'from'), the sociative-instrumental ('with' case), and the locative ('in'/'on' case). Of these, the ablative was retained and kept its name, and the functions of the sociative-instrumental and locative cases were folded into it – mostly: the locative also continued to exist for some words in Latin. In Greek, on the other hand, all three of those PIE cases were dropped, their functions being divided between the dative and genitive cases.
So the ablative was already one of the cases in PIE, the parent language of both Latin and Greek. It wasn't developed in Latin as a brand-new case, though it did evolve in distinct ways in that language.
This is a very abbreviated answer, which I will intend to expand on in the future (unless others get in there before me). The short answer is that the ablative didn't replace any earlier case - it dates back to at least late Proto-Indo-European (PIE), which developed a complex system of cases (including the ablative) best preserved (in general) in Sanskrit. Greek represents a simplification of the earlier, more complex, system, where the ablative function was taken up by the Greek Dative and Genitive cases. (So, in this respect at least, Latin is more archaic than Greek)