[CA] About to file police reports of domestic violence/threats in preparation of child custody case. What should I expect?

Location: Sacramento, CA

I put this off for a long time because I was afraid of the legal consequences of starting a custody battle, and the father is out of state(Florida)and mainly out of the picture, but I’ve reached the point where I need to take this seriously.

The father of my child is currently refusing to cooperate with signing the paperwork needed for our child’s passport. He is minimally involved(inconsistently reaches out 1-3 x/month, inconsistently sends money), yet he is demanding that I pay him $50 for his time to get the passport form notarized— even though I agreed to prepare all of the documents, provide stamped envelopes, give step-by-step instructions, schedule the notary appointment, and paid the notary fee myself. This is a control issue that will only continue to escalate. Because of that, I am now preparing to pursue sole legal and physical custody.

I am planning to start by filing a police report for a domestic violence incident that happened about a year ago involving the father of my child. During that incident, I was assaulted, and at one point I was holding our child while it happened. I also have an audio recording of him verbally admitting to it, along with additional threats of future violence that I intend to report. I am also considering filing for a restraining order.

My main questions are:

-What usually happens after filing a domestic violence police report in this type of situation?

-Since he now lives in another state(Florida), could this lead to a warrant for his arrest?

-Does this usually remain a report at first, or can it quickly turn into family court/custody proceedings?

-Should I expect immediate legal action or a court date once these reports are filed?

I am trying to understand what to realistically expect before moving forward. Also, if anyone has recommendations for strong child custody attorneys in the Sacramento area who handle domestic violence cases, geared towards mothers/women I would truly appreciate it.