You raised an interesting point. While there is the obvious source material in the comics, I always found that the animations would serve a more useful purpose for the building of a coherent "shared universe", because the animated series, like Batman's or Superman 90's cartoon had their own contained story arches, without necessarily falling into the intricated continuity problems of the comics counterparts.
i agree. the DCAU would actually be a good model to work on: make movies based on biggest and most marketable heroes--namely Batman and Superman, and maybe a few others (obviously, Green Lantern comes to mind since they made a movie starring him, and Flash could be another) and then make a Justice League movie which explicitly bridges them. it could even have a base set-up like the first two episodes of Justice League: ruins are found on Mars which are used as a covert invasion by aliens, Martian Manhunter is captured and brought to Earth, and during the first 30-45 minutes of the movie we're also introduced to Wonder Woman and maybe Hawkgirl (or Hawkman or some other well-known DC hero, maybe Aquaman) who then team up to fight the villains
however, i think it would probably be better if it was a more iconic alien threat which is used. which one immediately comes to mind, and who would already be established by a previous movie? well, several, actually, since both Superman and Green Lantern are explicitly associated with as many alien as earthly threats, but the ones that immediately come to mind for me are Darkseid and Brainiac, though i think Brainiac would make the best one, especially if he was introduced in the prologue to the Superman movie and, much like in Superman: The Animated Series, appeared in the stinger for the movie as having been recovered by random aliens (or maybe even a couple of unimportant Green Lanterns to bridge it with that other movie early on) to show that he survived the destruction of Krypton.
another bridging moment could be in a Batman movie which maybe has Lex Luthor briefly appear, meeting with Bruce Wayne (maybe he's on his way out as Alfred walks in to tell Bruce something) some other possibilities would simply be to imply possible movies or other team-ups like what the MCU did at the end of Age of Ultron, not only introducing a few new Avengers just before the climax but also explicitly showing some at the end even though they had no major role, namely the Falcon. a Justice League movie could do this with some lesser-known but still-recognizable characters like Green Arrow, Black Canary, Vixen, Doctor Fate, maybe Blue Beetle or even Nightwing (if they decided to introduce Dick Grayson in his own movie and have one of the other Robins in a later Batman movie--it could even be Jason Todd with him being killed by Ledger's Joker in the climax)