Use a Superman sequel to TRULY take advantage of a shared universe. Brainiac is the bad guy. Have Lois, Jimmy and Perry and Ma. Luthor and Brainiac meets at the end as, after the final battle, Luthor “saves” Brainiac. At Luthor’s side is Deathstroke andBlack Manta. The four give us a hint at a Legion of Doom founding.
Fastforward to Black Adam movie where Cheetah from WW1984 appears and hints at more LOD stuff.
Flash Movie has a similar scene with Grodd.
Then, you have Justice League: Legion of Doom movie which begins a bigger storyline eventually introducing Darkseid properly.