...The best that could happen would be the Referee, either through strong clues or implied threat (or direct threat, I guess), egging the Players along the the proper path to follow.
All of this was never that fun for me -- as a Player or as a Referee...
I have, at times, run "epic campaigns" - sometimes to the complaint of players who are much more interested in more mundane "lets make some money and retire" types of things. I think the biggest thing you have to do is get buy-in from your players.
Because nothing is more miserable that a bunch of players being forced into a certain style of campaign that they simply aren't interested in (or outright hate).
The other thing to keep in mind is that "epic games" tend to require epic characters - the old CP2020 Referee supplement Listen Up You Primitive Screwheads had a very nice breakdown of different power levels of characters in that game - and it is important to understand that in the respect, Traveller and Cyberpunk have a similar issue.
The "basic character" is not an epic character. You can get/make an epic character with the rules - but the basic, run-of-the-mill character is, well, a basic run-of-the-mill kind of person. Perhaps one with some fire in their belly, but not one that stands out compared to the norm.
So looking at how you want to tweak the chargen process to get your players characters that they believe are epic is also important. Maybe it is skills, maybe it is rank, maybe it's social class or economics - who knows, that is pretty dependent on your players.
But you have to get their buy-in, and you have to give them characters that they believe are capable of the epic things you are going to ask them to do.
D.