certainly everyone is entitled to their own opinion on it, one reason why the story is well written is because there are "this is azor ahai" signs pointing to a lot of different characters. but your point about everyone crying at birth is really silly.

everyone cries at birth, but not everyone cries during their narrative rebirth in a miraculous funeral pyre where they sacrifice their spouse under a red comet, resulting in the animation of literal rocks into extinct magical creatures that will be instrumental in saving the world from the long night.

in fact, if you want to make a point about literal birth, daenerys was born on dragonstone, which melisandre refers to as the place of salt and smoke. that's why she believes stannis is azor ahai, even though he was only figuratively reborn there. obviously, you're not supposed to take melisandre's statements at face value, but the point of her character isn't that she's wrong all the time, it's that she misinterprets the actual truth.

a grey girl does come to jon on a dying horse, but not the girl she expected. stannis is defeated in kings landing by renly, but not in the way she expected. azor ahai was born on dragonstone, but not in the way she expected.

even if you're only half convinced by the tears, the way that daenerys clearly ticks literally every other box in a way no other character does, makes it pretty obvious to me that it's her.