> What's the corroborating evidence from ~750BC documenting their existence? Heck, where's that evidence from 650BC?
This is a totally unfruitful line of inquiry, unless you are an academic historian doomed to publish-or-perish; in that case, it's perfectly understandable that you have to make these arguments as part of your career.
Better questions, when it comes to ancient history are:
1. Is there any negative evidence? 2. Is there any reason to expect more evidence than what we have? 3. Did ancient historians with better sources believe it? 4. Is there anything inherently unlikely about the idea?
In this case there isn't any negative evidence, there's no reason to expect more evidence than what we have, ancient historians believed various versions of the same basic story, and there's absolutely nothing crazy about it - someone had to found the polity, and to declare them fictional results in there still existing a first king of Rome, just a guy with a different name for whom there is no evidence at all. You can certainly apply (4) to specific details of the different stories - for example, it seems much more likely Romulus was murdered by Senators than raptured by Jupiter, though perhaps something altogether different happened. There's even very weak archeological evidence - a chamber was found in an area where Romulus' (empty) tomb was supposed to be, although archeologists are debating over whether it really is that.
> This is a totally unfruitful line of inquiry
It's really not. This is the line of inquiry that leads you to understand the founding myth of Rome and what the motivations might have been to create such a myth. It also helps to place in time when the myth was concocted.
> Is there any negative evidence?
Is there any negative evidence against unicorns?
Things that don't exist don't leave evidence.
But yes, there is evidence. The lack of corroboration and the fact that the earliest mention of Romulus was ~300BCE is a pretty strong indicator that he didn't actually exist. Further, the fact that his story is a mishmash of common tropes and that his very name is a derivative of Rome is a pretty strong indicator that he was simply a product of myth making. There are written records from surrounding nations and people from 750BCE.
But further, we also have evidence that Rome itself is a lot older than Romulus is supposed to be. There's evidence that the first founders of Rome showed up around 1600BCE.
The fact that the first records of Romulus trace the lineage of the rule of the city directly back to him is a very good indicator that the author was myth making.
> Is there any reason to expect more evidence than what we have?
Yes. People write about their leaders. It's quite common. And very influential leaders tend to leave pretty extensive records.
That's why, for example, we are so certain Ramesses II existed.
> Did ancient historians with better sources believe it?
You'd expect passing references to Romulus if they did. That doesn't exist.
> Is there anything inherently unlikely about the idea?
Yes, we have evidence Rome is a lot older than the Romulus myth. Seems pretty unlikely that Romulus founded Rome in 753BCE unless he was some sort of time traveler.
> ancient historians believed various versions of the same basic story, and there's absolutely nothing crazy about it
Ancient historians who wrote over 1000 years after the actual founding of Rome.
Imagine if I dubbed myself a historian and started writing about how China was founded by Jackie Chinamus in 1000AD, who also just so happen to have an army of pandas and consumed only bamboo. That is the problem with the Romulus founding myth. The historian placed the foundation WAY later than it actually was and wrote a fantasy story about Romulus where the only thing that could possibly be true is his name (Unless you want to claim it's possible Mars was his father).