I don't know if I can even post this, because it relies strictly on Legends Material, but the opening of Rogue Squadron (Novel) has Corran Horn being run through a simulator program. While this is post-Endor, it seems clear that at least for Rogue Squadron there is a clear training program that they use to ramp pilots up. The Rogue Squadron Comic Book series (which takes place even earlier in the timeline) even has a bank of X-Wing AND TIE Fighter simulators on board Home One that is used to weed out pilots and their skills.
Going back a bit further, Pre-Yavin, Keyen Farlander is trained using a simulator system that has him flying historical missions. This system is implied to be aboard a Mon Calamari Star Cruiser, though it's never explicitly stated as such. This also introduced the concept of the Pilot Proving Grounds, and if you completed enough back-to-back bases through the gates (which were on sort of floating platforms with turrets on them) you earned a proficiency badge for the ship you were flying. Navigating these platforms is pretty tricky - you have to engage the turrets and manage your speed while piloting yourself through the gates and around obstacles. While I would not say it's a close approximation of combat, the actions forced on the pilot are going to require developing similar skill sets.
It's never stated when exactly it was created, but there is a base on Folor that was dedicated to the training of new pilots, it is strongly implied in the Wraith Squadron novel that this base was established at some point after the Battle of Yavin. This base had a satellite field that the fighter pilots preferred and a canyon run that the Y-Wing pilots preferred. This base was abandoned shortly after the formation of Wraith Squadron.
X-Wing Alliance also details a little bit of this - the main character in that game is previously a cargo pilot (I would say smuggler, personally) who undertakes a number of training missions and spends much time in the simulator (again, it's implied this is standard aboard most Mon Calamari Rebel Ships). Some of his training also occurs at a semi-abandoned Smelting Facility that stretches between several factories and asteroids (this maybe the satellite feed from Folor? Wookieepedia says this was established 'shortly after Endor' with no annotation for the source of that information). This game takes place before Endor - establishing the existence (in Legends at least) of simulators aboard these ships well before the Rogue Squadron comics set them there.
And this is where a lot of the Rebel Pilots came from - Imperial Ranks, Smugglers, and Bush Pilots. People who already had a natural aptitude for flying and had been in some 'harry' situations (sometimes in the case of smuggler pilots [Lando Calrissian, Battle of Taanab] actual combat) that would prepare them for the stress of combat.