Should I File For Custody?

Should I file for custody if I already have the kids full-time and do everything alone, my kids are one and three. Their dad (my husband) left the country without telling us and hasn’t reached out in over two months, not sure if he’s coming back . I’ve hired a divorce lawyer, and she said I could pursue sole legal and physical custody. My concern is whether filing is necessary since he’s not involved or present.

If he does come back and we go to mediation I know he won’t agree to full custody for myself out of spite, not because he cares about his kids, and I cannot afford a trial. I just don’t know what to do. And if I don’t file custody ,I doubt he will reach out ,and I won’t have to deal with him vs if he had visitation or what not. Any advice would be greatly appreciated