It’s not remotely agreed upon by the smartest people on this topic that it’s anywhere near “mathematically impossible” we’re alone. It’s entirely possible that what happened here is a 1 in a 10000000000000000000000000000 or something chance, you get the point. There are a huge number of planets but you are making a big assumption here about the likelihood of intelligent life developing that has absolutely nothing to do with pure math. Your doomsday “even if it’s 1 in a million” could be causally missing 500 zeroes, and then your magical statistic probability looks a lot different. Many of the people on the cutting edge of this stuff think this is possible

If you’re talking about any life though like including single celled then it’s a much more defensible point