The cardio freak in my BJJ gym doesn't even run or do "cardio training" BS.
Dude just shows up and rolls. Hard rounds, technical rounds, it doesn't matter; he's always there.
Finishes every session with knee drops and sprawls.
The sport itself is the best conditioning.
Same with striking: heavy bag, pads, shadow rounds..
Far better options than a boring jog
Only thing I'd add?
Sprints.
Short, brutal, and closer to what actually happens on the mat than any jogging session ever will be.
Honestly the absolute best pre-workout aside from carbs and caffeine is actually warm-up sets
Makes you alert and gets your blood flowing
Always include at least 2 warm-up sets