The anthropic principle does technically work, but it admittedly feels like a cheat and I'd expect most audiences not familiar with it already would consider it such.

It's not a knock-down counterargument, but it seems to me we don't know enough about physics to say it's actually possible that the universe could be fine-tuned differently. Sure, we can look at a lot of fundamental constants and say, "If that one were different by 1 unit, fusion wouldn't occur," but we don't know if they are interconnected, and I don't think we can accurate model what would occur, so it's possible that it couldn't be different, that other constants would vary with it, and/or that it would make a universe so entirely different from our own that we have no idea what it would be like, so it's quite possible it could support life of some form.

Or, reduced into something more succinct, we don't actually know what the universe would look like if we changed fundamental constants (if this is even possible) because the results are beyond our ability to model, so it's quite possible that most possible configurations would support some form of life.

Multiverse works too, but again feels like cheating. I also admit there may be facts that undermine this, I'm not super-familiar with the necessary physics.