My problem with the fine tuning argument is why could our universe not have come about as a result of random constants?

Sure, it’s extremely unlikely, but that’s not how probability works. If every combination of constants is equally unlikely, an unlikely combination is the guaranteed result. Basically, no matter what kind of universe existed under different constants, it would be as unlikely as our current real universe. So we are observing exactly what we would expect if the constants were random.

If you shuffle a deck of cards, the order of cards you get is a result that is so unlikely it has never happened before and won’t happen again. Do you think that was intentional as well? Why not?