You probably won't.  It takes time for the moisture inside to work to the surface and evaporate.

All I can suggest is to aim a fan on it. If you can include a LITTLE heat (don't start a fire!) for the fan to blow toward it, it should help.

Use a faster-drying paint like tempera or acrylics, and aim the fan at the paint, too (no heat).

Good luck!  But start earlier next time. Papier mache is not an instant process.

Sue