Marvel Rivals is not currently planning on a PvE mode. While you can technically avoid going against other players if you just choose to play against bots (or if you lose enough to the point that you're put against bots), there's no dedicated PvE.
This is something Marvel Rivals' producer Weicong Wu confirmed to IGN recently, saying "for now we don't have any kind of a PvE plan, but our development team is continuously experimenting with new game play modes. So if we found that a new specific game mode is entertaining enough, fun enough, we would of course bring it to our audience."
As is the case with a lot of popular live-service games, while there aren't any plans right now, that doesn't mean there can't be any in the future. With seasonal events and such, we would be surprised if PvE really never came to Marvel Rivals, but so long as the player numbers remain high, it's unlikely we'll see a need for a winning formula to be changed.
