With (land!) crab tanks you don't need to establish bacterial colonies in a filteration system to cycle ammonia through the Nitrogen Cycle (TM); the crabs aren't in water where ammonia waste is aqueously supended, so their own excreations wont build up and kill them.
As soon as the air temp is in the ballpark & humidity is up, they can go in.
But you should of course clean up their poop. And use a dechlorinator that mitigates ammonia in tap water... because their bathing water is ingested and used to moisten their gills.
Preferably the tank is stable (temp and humidity not fluctuating much) before the crabs go in. If you can give it a day or two that's great - but if the crabs gotta move, then the crabs gotta move.
As for how long stabilization takes, it depends on the tank & ambient conditions. You may find yourself fiddling with heat & humidity for a while after setup (like if your ambient humidity is super-low, or if your room temperatures vary considerably from one day to the next, making consistent heating an issue). But as mentioned, larger tanks are much easier regarding stability.
