My advice is that if he doesn't care about the plot and the world at large, give him something smaller and more personal that he does care about that gets threatened.
In the case of Shrek, the one thing he cares about at the start of the story is his peaceful, solitary life in his swamp. That's the thing that is threatened that he wants to get back.
Most protagonists are driven by a "want" for something they believe will fix all their problems or complete their life, and then along the journey to try to get that thing, they discover the thing they actually need. The want is often something material like money, treasure a magical artifact, land, a house or a title, and the need will often turn out to be something more emtional or spiritual like love, friendship, community, peace, greater purpose etc.
So with an apathetic protagonist, the thing they want is usually everything to stay the same. They just want to stay in the place they live and keep on doing what they already do. So the thing that is most likely to drive them is:
- The threat of losing something like their home, status or income and being pushed into an unknown living situation and the desire to prevent it.
- An unwanted change to their living situation and a desire to undo it (the classic "and now a funny talking creature/ magical flying nanny is causing chaos in my orderly life!" in Mary Poppins or Paddington).
- Actual loss of something that brought them some kind of peace or joy sparking a desire for retribution (like John Wick).
- A major shakeup that changes their life in some way and makes them realise they must make the most of limited time (ie. they develop a terminal illness, they discover they have a long lost child or sibling).
- A genuinely real-sounding possibility to fulfil a dream they'd long since abandoned, but the idea has them hooked.