How can I get full custody or sole custody?

My son's father abandoned us for 6 months on a drinking and partying hiatus. I tried calling but he wouldn't answer the phone and he went to a different state, so no matter how hard I tried I could not get in contact with him. I resorted to calling his best friend to reach him. Although they live in the same house and his friend would tell him it was me on the phone, I could hear him refuse to answer. Eventually, he lost his job and has spent the last couple of months homeless. Now, he claims he's been sober which probably means still heavy drinking. He got a new job and wants to be in my son's life. I don't want him around. I know its only a matter of time before he is drinking and getting high again. I was with him for four years begging him to get treatment but he never did. Unfortunately, the only proof I have is an email where he apologizes for the domestic violence he inflicted on me when he was on drugs. Is there any way I can at the very least prevent him from having alone time with the baby? At best I would like to have sole custody. The baby was born in Arizona. After he abandoned us (moved to MN) I moved in with my mother in Colorado.