A child born abroad can acquire citizenship at birth when the citizen parent meets the applicable residence, physical-presence, parentage, and date-of-birth rules.
Sources: U.S. Department of State — Citizenship at birth abroad
Federal statute grants citizenship at birth to a person born in the United States and subject to its jurisdiction.
Sources: U.S. Code — 8 USC 1401
A permanent resident married to and living with a US citizen for the three years before filing may naturalize after three years, instead of five.
Sources: U.S. Department of State — Citizenship at birth abroad
The standard route requires five years as a lawful permanent resident and at least 30 months of physical presence in that period.
Sources: USCIS — Naturalization for lawful permanent residents