Can you dry out a wet matress?

I have a few times. Just toss it out in the sun. They actually dry pretty fast.

If the mattress is fully saturated, it may not dry out well before mould starts to grow.

Yes, @Dr Lawrence

If it is saturated deeply, I would put it in the sun, which kills bacteria also, but, I’d also maybe soak it again in that spot with a disinfectant which would prevent mold forming.

Depending on it’s thickness you might want to really blast it with some sort of bleach solution or Lysol maybe.

I think it really depends on the mattress. If it is one of those sponge mattresses and it soaked all the way through, then you may have a problem with mold growing on it. I would ask a furniture cleaning service. Even if its partially hollow, moisture can remain inside and grow mold with the heat and the darkness. Bleach would destroy the fabric on the outside and eat the foam away.
If you do intend to keep it. Air it out for at least a week and then cover it with a plastic cover to prevent mold from coming to the surface and making you sick.
Even if it doesn’t come to the surface, mold spores can get through and make you sick before you realize it is the mattress.
Best be careful. Hire professionals.

Yes, but I would reposition it frequently. Here in my neighborhood, the heat would dry it out in record time, we had over 100 degrees today.