I agree that soldiers don't stage a coup on the orders of a general alone.

You need a general with likeminded officers, and a convincing excuse for the rank and file to go along with their officer's orders.

Something like "the election was stolen, the winners weren't legitimately elected, we've got to defend our country". It doesn't need to survive detailed scrutiny, a few hours is long enough for the major scrutineers to accidentally fall out of windows.