The child born abroad to an LPR mother during a temporary trip abroad, can enter the US as an immigrant without needing an immigrant visa, if brought to the US within 2 years of birth accompanied by an LPR parent on that parent's first return to the US after the child's birth, as described in 9 FAM 201.2-3(b)(2). However, that doesn't help this case since the mother was not an LPR and only the father was an LPR.
So it seems that the child will need to get an immigrant visa, either petitioned by the father as the child of a permanent resident, or as a derivative beneficiary of the father. Generally, a child must be born before the principal beneficiary immigrates in order to be able to immigrate as a derivative beneficiary, though 9 FAM 502.1-1(C)(2)(b)(2)(C) mentions that a child born after the admission of the principal beneficiary, but who was "born of a marriage which existed at the time of the principal applicant’s admission" can still be a derivative beneficiary. I am not sure if the parents were married as the time the father immigrated, but if so, Consular Processing for an immigrant visa as a derivative beneficiary might be an option for the child. Otherwise, the father will need to file a new I-130 to petition the child, and wait for it to get approved, before the child can go through Consular Processing. Either way, it's going to be a long process before the child can immigrate to the US.