Well, recall how long it took from FC-31, through FC-31V2 to eventually the J-35 prototype. I recall back in 2012 or so one of the first artworks of FC-31 was carrier based. This is not to say that a similar time could or should ellapse until the J-50H prototype, that was a mistake as i pointed with other occasions, hopefully the great delay/diddle-dwaddle in the case of J-35 won't be repeated, but there might be a few years until a J-50H could fly. Ideally several prototypes or even LRIP should be timed with the commissioning of the 004 CVN.
A 3rd bespoke carrier 6th gen fighter is possible, but imo even for China that's probably too many 6th gen airframes, the 5th gen only has two, the 4th gen only 2 as well etc. But whatever they do, they need a 6th gen carrier fighter just as badly as they needed (hence the fast development) 6th gens for PLAAF, in order to compensate to the still great numerical disparity vs the USN by having a superior fighter, disparity which is even worse than for PLAAF vs USAF.