It was wrong of me to suggest your rebel player needs to play better. I apologize.
I’m trying to figure out how all these things can be true, though. If the Empire is stopping Rebel missions, they’re not moving troops around. If they’re covering half the board, they aren’t stopping missions. If they’re pursuing their own missions to dig deeper into the probe deck, they’re either not stopping the rebels or they’re not moving on the map. You only have 6 leaders by turn 3; you can’t do everything.
Stumbling into the base on turn 3 tells me he put the base way way close to the Imperial front lines; you literally cannot get to the backmost worlds unless you beeline right toward them, ignoring everything along the way. Did you guys play with the starter map or set it up for yourselves?
Finally, the Empire’s forces are split like 5 ways when the game starts (assuming you’re using the starter map). By turn 3, the Rebels will have had a round of production and should be have been able to trivially stop a ground attack.
What I don’t know from personal experience is how moving your base looks. I suspect by turn 3 or 4 there should be plenty of map left to move to, but that’s definitely left to the draw of the cards (draw 4 to remobilize, hope they don’t have loyalty).
So…yeah, I think several things could have gone just right: you could have beelined right into the right world with a very large ground force, not stopping to subjugate anywhere, and they could have drawn a truly terrible hand of new base options all of which are near ground forces equipped with transports, and then those guys could have immediately pounced on the new base. That’s a lot of things going right at the same time. There’s no beating bad luck.