Here's a few options, off the top of my head.
Rip van Winkle it. This is what the old Buck Rogers franchise did (games, novels, comics, computer games, and so on). TSR (which later on got bought up and became Wizards of the Coast) has an old setting called Buck Rogers in the XXV Century that does a new twist and setting for the Buck Rogers property - a setting which I enjoy tremendously. It's transhumanist, STL, and no aliens.
Dimension jump it. Basically a variation of any number of tropes, but the end result is that the characters are part of a dimension jump technology thing (similarly as to how Marty McFly was shanghaied in the Back to the Future movies) - either under their control or through happenstance - and are likely to spend their time looking for a way back to their own dimension.
This can also lead the way into a different sort of campaign - the StarGate SG-1 campaign. If your guys have no way of getting to a place except for through a Stargate, and you just remove all the extra races but keep the humans, that should fulfill your requirements.
Do a The Last Starfighter. In this most excellent movie, the protagonist is very good at a specific video game - which turns into being a recruitment device for a side in an interstellar battle that is currently losing. Just remove the aliens, keep the overall concept (i.e. that the characters are very good at something - but completely clueless about the larger issue), and go from there.
Your suggested start sounds a bit like the Cowboys vs Aliens graphic novel. Not that there's anything wrong with that (except the movie - which didn't do the graphic novel justice). You can also pull a Flight of the Navigator, where there's a kid that finds a space ship (but just say that the Ancient Astronauts 'theorists' were right, and there is an ancient Human civilization out there), or perhaps a scenario more like Explorers (or Species or Contact, for that matter), where someone on Earth gets information transmitted to them that allows them to build a starship.
(For extra fun, I'm imagining a group of rednecks that gets something like this beamed to them, and manages to build it out of an old RV, a large water tank, and some bits and bobs - and goes into space, the Final Frontier, very heavily armed.)