To enforce an ideology you need people whom identity is based around the ideology, they need to be losers, goons who don't have anything else for them going on.
Therefore the proper military can indeed be an attempt to de-escalate the situation.
Considering that our military swore an oath to the constitution and to defend the country against domestic threats the correct thing for them to do might instead be an escalation against that alternative force of losers operating in American cities. I wouldn't bet on the military occupiers marching into Minnesota upholding their oaths though.
Further, under the current regime, you have to remember that military leadership and checks and balances has been systematically eroded for the last 12 months. Military leaders that would oppose trump are/have been removed or retired. Holsey is the latest/biggest example I can think of. Look what happened in Venezuela almost immediately after.
Also, recall the address Hegseth and Trump gave to the gathering of generals in Quantico. They explicitly said if you aren't an ideologue aligned with the administration, there is no place for you in the military. Which is to say that the time of the US military being non-partisan is over.
Lastly, I'd consider the kind of leadership Hegseth and Trump want leading that occupying unit. It's going to be somebody that will be receptive to their orders, legal or not.