SPECULATION Title might be misleading...

What about Dantooine?

 

That'd at least sort of work. The only problem with that is, it had been "deserted for some time" when Leia gave up the location to Tarkin in ANH. The way the opening crawl was worded made it sound like the Rebels' "first victory against the evil Galactic Empire" had just occurred, if not within hours of the beginning of the movie then certainly within days or, at most, weeks. Had they launched their attack from Dantooine and then abandoned the base, it would have looked freshly abandoned when the Imperial scout ships reached Dantooine following the destruction of Alderaan.

So while it would work in the most technical sense, since the Rebels were apparently, once upon a time, based on Dantooine, it just doesn't fit nearly as well as simply having that first Rebel victory launched from the Yavin base would.

 

The beginning could be the move from Dantooine to Yavin IV. Landing on Yavin IV they could stumble across the ruins of the Azure Angel, too.