The short answer is “I don’t”.
I don’t know with any true level of objectivity that the gods are real. But there are days when I’m not even convinced that I’m real or that life is real, so there is that to consider.
The closest I can come to is comparing the experiences that I have had, plus the experiences of others and noticing trends and weird freaky unexplained shit. Looking at things that lined up freakishly close to historical references that I was unaware of. Or looking at weird happenings that could confirm that I’m not pulling this out of my ass. Stuff that’s happened that isn’t easily written off or explained as coincidence.
Problem is, my brain will always find ways to write these things off as exactly that- coincidence. I will likely live my entire life questioning if I’m just experiencing one long, drawn out acid trip. Such is life, I guess.
But at the end of the day, no one can really objectively prove that the gods are real. It’d be cool if one day we could, but today is not that day. And I fully accept that I have no way of completely proving it to myself, let alone others. But because of that, I don’t really know without a shadow of a doubt. And I’m okay with that.
So therefore, my answer is “I don’t.”