Hi,
Unfortunately there is no way to tell MMW to wait for spinup it is system process and not controlled by MM.

Depending on the Output Plugin you may also be able to increase the buffer so it may be long enough for the disc to start.

A solution:
Do not use pause for extended periods. Shut down the program and restart when needed.

Step 1.
Play music using Media Monkey.
Step 2.
Pause for an extended period of time.
Step 3.
Hit Play...
At this time, the hard drive is usually shut down. When I hit play, Media Monkey will play what is in the buffer, about 2 seconds worth. Then playback stops while it waits for the hard drive to spin up. Is there a way to tell Media Monkey to wait for the disc to spin up before attempting playback?

Windows 10.0.18362
Media Monkey 4.1.21.1875

The music is on an internal hard drive. (My system drive is an SSD.)