I briefly played Ludia’s dino park builder game and they had some sort of a “PvE” content… here are some suggestions
Storymode: a mode where you have some semblance of story + battle against AI that get progressively harder as you win. Perhaps each level has a specific 1 time reward for winning (i.e. 1st level, you get a 15 min incubator, 2nd level = 20 vraptor dna etc) and the reward gets better as you go higher
Themed dungeons: maybe a rotation of themes such as “must be slower than 120” or “must be a four legged” or even a multiple restrictions! Again, these dungeons could be either (or both!) PvE and PvP
Raids: once they implement a guild/clan or even friend system, perhaps they will allow a “dino hunt” or something along those lines? Perhaps even fight a mega-boss-like dino as a group?