My Daughter's Father Won't Let Me Move With My Daughter

Hello I need some advice.

I live in San Francisco, CA. I am supposed to be moving today to a new apartment that I was able to find for me and my daughter. I had been living with my daughtee and her father in the same house for the last few years. I care about him, but I don't love him anymore and I want to move apart and create our own space, so my daughter can thrive and know what a happy couple looks like. (We argue a lot and my daughter is now old enough to comment on it). So I find a place that is perfect and I told her father about it last week. I understand that he would be hurt, but he has absolutely refused to talk to me about how we are going to split up her time. I have written out co-parenting agreements, told him let's go speak to a mediator and even said that she can stay here while I get the place ready. I tried to offer one week on, one week off. Splitting up the week, but he won't listen to any of it. I spoke to a law group the other day and they are going to help me file for custody since he forced my hand. However, I am suppose to be moving today and since I haven't filed yet because the law group takes about 7-10 business days. I am wondering what I should do. Should I hold off on moving until I opened the case? Should I go ahead and move by myself? Should I get cops involved for me to move with my daughter? That isn't my favorite option since I don't want to stress my kid and I feel that it will make her father even more closed off to mediation? I need help. Thank you

Edit: juat to clarify...my daughter isn't in any danger with her father. He is just super attached to her because he doesn't have anything else going on in his life right now.