Really a hit or miss concept, military coups.
The USA has the best government that money can buy.
Countries don’t have military coups or juntas because they are fundamentally bad or whatever. It happens becuase controls and civil authority is too weak, and we are in a cycle where the US is dismantling all controls and adopting a position of unlimited executive power. So it’s a matter of “when” some general intervenes. Either at the behest of someone or to save the republic.
You don’t really need a lot of people. Maybe a battalion or two.