I have a Q style Square D service box and the wire will be coming in the bottom.
Can I mount the box with the inputs and the 200 amp breaker down?

The handle of the Main Breaker must be oriented so it is up in the On position, or down in the Off position.

Most newer panels have the main breaker oriented with a side-to-side movement. They can be mounted either breaker up or down.

If it is an up/down main breaker throw then follow TK's instruction.