They should at least ensure the EMALS is working properly as well as the nuclear reactor before doing 004.
We have no evidence of land tests of nuclear reactors of the appropriate characteristics having been done.
The pebble bed reactor which recently became operational has the required capacity but the technology would be ill advised to use in a ship. The land based ACP100 reactor will only be built in a couple of years. There are no news on the navalized ACP100S either other than that its construction was approved. Given this I expect construction of a nuclear carrier to start no earlier than 2025.
What they could do is build another 003 carrier. Which is what I suspect will happen. We had rumours a couple years back that they were going to build two conventional carriers of 003 type with two different block construction techniques in different yards to see which one would be more effective. I suspect that is what will happen to retire risk on future large carrier construction and increase the amount of boats they have to train airmen before the nuclear supercarriers hit the water.