No, cockroaches are not born pregnant. It takes about one year for a baby cockroach, called a nymph, to develop into an adult and become capable of reproducing.
Cockroaches don’t become pregnant, but rather they lay eggs in sacks of about 40 eggs each, and after about six weeks those eggs hatch into cockroach nymphs.
When the cockroach becomes an adult after about one year, it may lay several egg casings before its death. Most species of cockroach have a life cycle that lasts a total of about 1 1/2 to 2 years.