In my practice I have argued for clients on both sides of this issue and it always gets down to the facts of the particular people in the particular case. California does not have a specific law but allows the judge to decide whether it is appropriate.Issues relevant to a judge in my experience include to the age of the father, any other children he has helped raise - if any, his involvement with the prenatal care, care of the baby prior to the parents separating, support he provided during pregnancy and since that time, his aptitude, his intellect, any issues he might have with drugs, alcohol, unemployment, instability, abusive personality, etc.
The judge also reviews, whether or not mom is being reasonable with trying to allow the father to nurture a familial bond, what she is doing, how she is responding to the logistical requirements to move the child back and forth, etc. The court might also consider his family and extended family and whether they are involved constructively or destructively in forming a bond with his side of the family and the same issues concerning your side of the family.
I have seen many situations where a specific overnight is held or two and then a new hearing after that time is scheduled to see if there were legitimate problems or to green light regular overnights.
Assuming a father has been involved in parenting and has maturity here say 22 or older much more likely they get an overnight at least a trial.If the father has known issues here be it with drugs, alcohol, instability, prior convictions then there be reason to delay overnights.But with a normal adult that has had interaction with infant the judge may at least grant a trial visit.Even if mother is breastfeeding pumping can be done to store the amount of nourishment for the child.
That is as definitive an answer as I can give you under California family law and practice.Please let me know if you have more follow up based on this.Thanks again.