Bear with me it's literally upto convenience of my plot. Marvel and Dc events are almost from same sequence with changes due to more heroes and villains.
General goes as-
Kryptonian invasion (man of steel)
Iron man(Lex Luthors hostile takeover attempt), Thor(Dr Fate gives guidance), Hulk etc 1st appearances
Death of superman (batman vs superman)
As a trigger from his death and rainbow bridge's destruction Chituari invasion(Avengers) following Steppenwolf on Darkseid's conquest (strangely neither Darkseid or Thanos butted heads against each I wonder) with remaining avengers and shield contributing in it .