I am a US legal permanent resident, and I just had a new baby.  Is my son/daughter automatically an LPR or a US citizen?
If your child was born in the US, then he/she is a US citizen.  You may use the child’s birth certificate to apply for a US passport at any US passport office.

If your child was not born in the US, then he/she may automatically become a legal permanent resident under the following conditions and does not require a visa to return to the US:
a)The mother is a US legal permanent resident;
b)The child enters the US within two years of birth;
c)Either accompanying parent is applying for readmission upon first return after the birth of the child.

If the above conditions do not apply, the US legal permanent resident parent(s) may petition for their child to immigrate to the US by submitting an I-130 petition to USCIS.