Thing is, Hungary has pretty balanced teams, but no individual standouts like some other Group C nations. That's why team qualification was actually more likely than an individual one (especially in jumping).
Looking at the current individual rankings, there is no chance in jumping.
Balasz Kaizinger currently holds a quota in eventing, but that's still very much an ongoing battle.
Even though he is out of it at the moment, Benedek Pachl in dressage might be the best bet actually, provided he collects few more high scores. Plus few more nations are bound to qualify teams so he will move up in the overall allocation list.