Can my husband file for Custody in AZ, while my step daughter is here visiting? There are no current custody orders established

The first questions are what do the existing orders say about parenting time and custody (now called legal decision making in Arizona) and does dad have a copy?   The court typically calls this the current order, regardless of how old it is.    The specific terms of the warrants will also be important in knowing how significant the emergency is. The next question is whether there is a jurisdictional issue.  If the current order is in California or if the child has been living primarily in California for the past 3 years, California may have jurisdiction (the right to enter orders regarding your child).  But, if the emergency is sufficient, it may be possible to address this in Arizona.   I am not clear if Mother knows the child will be having parenting time with you in Arizona.   I would strongly encourage you consult with a family law attorney in Arizona where you live who has experience with what we call UCCJEA and UIFSA -- these are laws that are used when the parents live in two different states.  I do have that experience.   When you consult with an attorney, bring all documents and information you have for the current orders, the warrants, and so forth.  If you do not have these, meet with the attorney anyway as it appears you have an opportunity to begin addressing this in the first 2 weeks of August.