During which lifecycle stage do cockroaches first emerge as adults?

Cockroaches first emerge as adults from the nymph stage. After the egg stage, where the eggs develop and hatch, the resulting nymphs are small, immature versions of adult cockroaches. They go through several molts during the nymph stage, gradually developing into adults. It is in this nymphal stage that they begin to look like fully formed cockroaches, but they are not yet sexually mature until they complete their growth and molt a final time to reach adulthood.

Therefore, the answer is that the adult cockroaches emerge after the nymph stage. Each successive molt allows for further growth and the development of adult characteristics, culminating in the emergence as fully grown adult cockroaches.