For example, some sources say it starts around 1100 BC with the Greek Dark Ages, others say it starts 776 BC with the start of the Ancient Olympic Games. And some say it ends when Greece was conquered by Rome in 146BC, others say it ends around 500 BC. That's a pretty big difference, and some other sources have other dates also.
On the other hand, Ancient Rome has a pretty concrete timeline spanning from 753 BC-476 AD. (Start of Kingdom, to the fall of the Western Empire)
What I think is the answer is that there was no unified entity of "Greece" like there was one of Rome, so the concept of Ancient Greece is basically a loosely tied civilization of Greek-speaking communities, so it would make sense that it's exact emergence isn't concrete.
Correct me if I'm wrong, this is just something interesting I have obsversed.
You are basically correct.
First, fair to note that the date of Rome’s foundation is based on much later, very mythical histories, and archaeology produces a much more complex and ‘fuzzier’ picture there too.
But Greece, as you say, was never just one single city with an official foundation date, and goes back to deeper prehistory.
I don’t think anyone says that Ancient Greece started with the Olympic Games. That was the basis of a dating system often used in Ancient Greece (again, not so clear their own dating was accurate…). But of course Ancient Greece existed before that.
Greece as a region obviously goes back far before humanity’s presence there. Greek human prehistory goes back to the Palaeolithic, and anatomically modern humans have been there for tens of thousands of years. Some level of civilisation there goes back to the Minoans (and Cycladic and Mycenaean cultures), whose culture developed gradually from advanced Bronze Age ‘pre-civilisation’ to a literate civilisation under Middle Eastern influence very gradually from around 3500 BC to the 2000s BC. However, this depends on what is meant by ‘Greek’!
Many other historians would consider most of the early inhabitants ‘pre-Greek’ for linguistic reasons, and then we might define Greek ethnic identity to apply to the first speakers of Proto-Greek (not that they ever used that outsider word for the whole Hellenic people, though possibly a north-western subset - nor that we have any record of them using it this early).
But this was also in prehistory, and hard to date or even define: the split from ‘nuclear’ Proto-Indo-European or maybe a transitional subgroup (lots of contentious discussion here) and the development of traits usually considered defining of ‘Greek’ can be estimated to the late 3rd millennium BC to the early 2nd millennium BC, and to a time they were migrating into the region but from archaeological and genetic continuity were likely not the only cultural group there.
You can’t compare all this to the foundation of a City. And the origin of a people isn’t the same as what calendar they use (much of the Western world pedates 1 AD, after all) and even in Greece other dating systems were certainly in use.