How long does a Mac take to boot after reinstaling Mac OS

The solid Apple is not in the Mac's ROM at cold start. It can only appear when you load the first 'blob' of software after Restart. so the drive can produce at least one blob of software from a know place. The next step is to load a whole lot of files by name, so the File System is initialized and the drive is Mounted.

If the drive can not be mounted, a file system check is initiated, and the progress bar is extended while this takes place. Failure to Mount AND failure to check out properly will cause your Mac to give up and power down.

Failure to make progress is typically caused by Bad Blocks on the drive (or possibly a kernel panic). Re-reading a marginal block can take up to a quarter minute per marginal block, worst case.

if you have been looking at the Apple logo for move than fifteen minutes, it may be time to power off and try to boot up again.

It is not unusual for a reinstall to take up to an hour before it finally boots up and ready for use. Are you getting a progress bar or any indication that it appears to be stuck?

The re-install process can be quite complicated, and there may be MULTIPLE automatic restarts along the way.