You may be able to leave without a passport, but you may not be able to enter another country without one.
Since Zimmerman was born an American, there’s no guarantee that he could stay in Peru. I don’t know the laws, but Peru is Peru and not America.
From Wikipedia:
Those children born overseas to Peruvian mothers or fathers who were not registered before reaching 18 years of age can acquire Peruvian nationality by choice if:
- A petition is made to the Directorate of Naturalizations and Immigration (DIGEMIN). For this the petitioner must be resident in the Republic of Peru.
Foreigners can also acquire Peruvian nationality, including: