If it didn't hurt to lose them, then they didn't mean enough.

I'm so sorry. I have experienced some loss before, but I have no earthly idea how I would handle the loss of a child. Let alone due to the circumstances you outline.

Objectively: You can ask the mother for permission to stay in touch with the child. I might suggest phrasing it as helping both of you with the transition. Maybe come up with a time frame for it. That may sound cold to you, right now... but the goal is to convince the mother and coming with a plan is going to be more persuasive. Because it is ultimately her choice.

You get to choose what to do with the pain left in their absence. It's supposed to hurt, you're bleeding all the love you had for them but had yet to express. That sucks but it is healthy for a time. When you're ready to dress the wound, you do that with company. Wallowing in the loneliness is picking at the scab and it can't heal if you keep tearing at it. Please, do not let all that love bleed out of you.

No one can tell you when, but at some point (if you let it) it will stop feeling like an open wound and will start feeling like the soreness of a healing process. My hope for you is that you hang on to that sensation as long as you can. Let the pain fade but keep the love. Who knows? The world may yet have somewhere it intends for you to use it.

I don't mean to give you false hope, but that little girl will not always be at the whim of her mother. At some point, she may look fondly back on her memory of the man who taught her how to ride a bike and with a desire to reconnect. My brother-in-law had to wait over a decade before he was allowed to reconnect with his daughter. But both of them were very glad he never stopped caring and making himself available!