Cortez and Pizarro won because they were able to take out the leadership, and because they had the boats to get to where they needed to be.
The question for the Marines, has to be where? Rome was big, much bigger than the Incan or the Aztec empires. They also had naval supremacy. The Marines, as good as they are, how are they going to get across the Mediterreanean? You can’t exactly fit an Abrams on a boat and sail it across the med, not with the technology back then.
Two things, one.
The Romans were good, really good, at political cohesion and negotiation. For the longest time they didn’t fight wars, except against Carthage. Since you’re dropping them in against Augustus, good luck with that. The military deployment in 23 BC, would be after the defeat of Antony and his consolidation of power.
If you are going to win, the Marines would have to figure out a way to kill Caesar Augustus, and take over a legion for themselves. Then, they could probably do some serious damage, but it would take years to consolidate control.
Two, co opting works both ways. If Octavian gets wind of a unit of men with technology far beyond his own, I wouldn’t be surprised if Octavian’s response was to march to meet them personally.
With women. Meet the marines in parley and make it clear to them that they are stranded without any options. Give them options, give them a way out, give them a villa, or command positions if they would swear loyalty to the Emperor.
How many of the typical marines in the typical unit are going to say yes?
Righto. If they’re actually stuck there, which makes more sense: trying to conquer a massive empire, which IMO would be utterly impossible. Or accepting positions of wealth and power within that empire.