That's not the NPR from game creation. There are three kinds of aliens you can encounter in-game:
1. Spoilers. 'nuff said.
2. NPR(s), who "mirror" yourself. Except they had an TN-start even if you had an conventional start. The NPR will be exploring and growing so when you encounter it, it should already have an star empire going on.
3. "Minor" aliens, that are activated only when someone visits their homesystem. During game creation, you set the percentage - 30% being default - of live happening on a suitable planet. This means that the first time a player or an NPR or spoiler comes across a Terrestial world, there's a 30% of chance of an alien race getting created. These aliens are always one planet-bound to begin with but they can expand beyond their homeworld and -system. Some might be technologically backwards, so they are no threat - others might be fairly advanced.
If you kept the "create random aliens as NPR" toggle on, then once these "minor" aliens have been activated, they behave exactly like NPRs and you cannot mess with them through SM. So it's entirely possible that while you turtle for 50 years in Sol, the NPR activates a dozen "minor" aliens plus maybe some spoilers and many of these then proceed to explore and thus activate more.
At least, such is my understand of how the system works.
I always do conventional starts. If your economy is running smoothly - the first hurdle - then it's time to build a military. You don't want to get caught with your pants down. Create an ideal task force, decide what sort of ships it needs, then jot down what components such ships needs and then go researching. I have an Excel-spreadsheet for that, where I turn components bold as they are researched. This way when I actually design the ships, I won't be missing a powerplant or that my Beam Fire Control is too small for my beam weapons et cetera. It's also good idea to jot down a basic, common speed for your task force, ie "all ships must go at least 3000 km/sec or faster".
Finally, as others have stated, you cannot overhaul your ships too often. Build at least three task groups - one will be in overhaul, second will be doing taskforce training and third can actually go on missions.