custody in California

I know every situation is different. But in general what is custody like with a newborn? Dad claims he should be able to have him overnight right away and I told him absolutely not. Am I wrong for this? Idk a mother (a good one at that) that would just let her newborn go stay at the dads right away..... I'm a first time mom. I'm 20. And the dad is a joke. If we went to court for custody in general what is the usual outcome?