I'd start with the original seven, formed at the end of the Superman film. I'm picturing Supes giving his first epic speech to the world about how he plans to right the ship and restore the meaning behind the cape, montaged with him around the world visiting familiar silhouettes, ending on a shot of the backs of the seven (so they don't have to be cast just yet), his legacy, ushering in the new age.
(Actually, given Kumail Nanjiani has been hanging with the Superman cast, I have a theory we're gonna see the 25th or 31st century in the film, perhaps as a framing device at the top and tail, as a museum janitor (Booster) recounts the tale of the world's greatest hero, ending the film on a shot of seven statues)
Then in subsequent films/series we could have references to the JLA, like in Lanterns where we have mention of Hal fighting Starro. Or the Authority being formed by those who get ish done in a way the JLA won't. Or the Waller series being about her trying to gain a modicum of control over the JLA, secretly blackmailing Batman, creating contingencies, etc (a set up for a Tower of Babel story).
And then come the JLA film, which probably won't be till like 2029, after years of operation, we can introduce lineup changes if they haven't happened already:
-Wally stepping into Flash's boots after he goes MIA (in time) at the start of the film. Our POV character, mindblown when he enters the Watchtower for the first time.
-John filling in for Hal, whether he's dead by the end of the Lanterns series, or just busy out in his sector.
-Hawkgirl being brought in to replace Aquaman doing King stuff.
Part of the story of the JLA film can be Superman's trepidation that the JLA may go the way of the JSA again if they let "just anyone" in (Hawkgirl specifically, given their previous meeting) to his deliberately small team, the ones he personally felt comfortable standing side by side with. But given the scale of the Centre, dozens of heroes and factions will have to come help to save the day, and by the end Supes could make the call for the JLA to open their ranks, inviting dozens into the Watchtower ala JL Unlimited, including Guy Gardner, Terrific, etc, and of course, Booster Gold.