It's entirely possible
Just becuase it was the 8th laid down doesn't mean it wasn't the first completed, "small" carrier like that could be built in a larger dock along with one or two others. It would save time
By sequence Earth, I meant you build a drydock with maybe two sections, one for each of two carriers, which are built simultaneously-not meaning that they are completed at the same time, necessarily.
As one is finished, the next is started.
So as CX-01 launches, CX-03 is laid down. Once each hull is completed, the ship can move out of dock for testing weapons, engines, shields and so on, while taking on various equipment like computer terminals and fighters, shuttles, crew accomodations and whatever else needed for a shakedown cruise.
This can be done quite rapidly if the hull is modularized and various components are assembled or "contracted" to smaller yards within the same system, and joined at a large facility or cluster of drydocks like Trojan 4.