So this ends up being a bit of an example of demanding evidence for an assertion that was not posed. So instead, and if we stick to the proposition, itself, what is the evidence that supports it? And what is the evidence that negates it? And is there any other evidence that would further clarify it? Without going into a whole dissertation, the evidence that supports it is the mystery itself. The existential questions of source and purpose are being "begged" by our reality, and are NOT being answered by any other logical possibility. So that even though we can't define this source/purpose, we can logically determine it's necessity.
The second bit of evidence comes from the fact that we are asking about it, at all. And not just 'we', but all humanity all across the globe and throughout all human history. That not only enforces the idea of logical necessity as mentioned above, but of something even more interesting I think. And that is that we humans have developed a cognitive nature that MAKES us ask. Such that it's not just ourselves asking, but existential nature, itself, is asking, ... through is. We are designed by nature to NEED these answers. To seek them. Very interesting, that.