This seems like a question that's impossible to answer in a historical context. "When did this start" is essentially an impossible thing to prove, given that this practice has roots back in pre-civilization in a few different contexts.

Obviously, the practice is commonly associated with religious rites, but it's also anthropologically viable in that there is a biological reason to 'cover up the dead'. Namely preventing disease. This would quickly become important once humanity transitioned from the nomadic to more permanent settlements, and obviously there is no historian I can give who was around to cite that sort of thing.

The Shanidar Cave in Iraq was found to contain bodies that are anywhere as old as 35,000 to 65,000 BCE and exhibit the signs of ritualistic/ceremonial burial. So as you can see, all we can really do is shrug and say that it's almost always been a thing humans have done.

I'd try r/askanthropology if you don't get answers here.

First, not everyone does. There are many cultures and societies that do not use burial as a means of disposing of the dead.

That said, asking "why" is complicated because you're talking about a practice that has such a deep history that there have probably been many "whys" over time.

It's possible, perhaps even likely, that it began as a practical means of dealing with the dangers of carnivores / scavengers. The fact that burial seems to have been practiced not only by anatomically modern humans, but also by Neanderthals, suggests that it has a practical utility that goes well beyond any ritual practice, at least insofar as it was done by more than just anatomically modern humans.

But that aside, the oldest (that I know of) anatomically modern human burial that shows ritual practice was a paired woman / child burial at Qafzeh (Israel) that's about 100,000 years old, and included red ochre. The interment of the dead with burial accompaniments implies ritual practice, not just a functional explanation.

In reality, it's impossible for us to say "why" burial first started. And it's impossible to say "when" it first started, because it's not likely that we've found the earliest burials.

We can say that anatomically modern human burial as a practice dates to at least 100,000 years in at least one part of the world, and that by that time, it appears to have had ritual practices associated with it.