Military is the only way?
If the Joint Chiefs wanted to act now, could they? No. Why? Because a legally appointed Commander in Chief exists up until exactly noon on the 20th.
At this moment they can only act on Trumps orders. They are waiting for an order that isn’t coming. Bear with me.
However, at exactly noon authority transfers to a new President, IF one exists legally.
If the military knows a President was illegally sworn in, are they obligated to obey? No. Their oath is to the Constitution.
So... at exactly noon the military, for the first time, has independent authority to BEGIN certain actions, in the absence of a legal President.
What actions? Whatever actions necessary to see that a new lawfully appointed civilian government is put in place.
Except that the military leaders are all jonesing for their next war, and they know that Sleepy Joe will be happy to give them one. Why on earth would they try to keep him from taking office?