Hi;
This is my first time posting in this section, so we haven't been introduced. I hope it's OK; every section seems to have its own etiquette.
On your question: I've had a similar dilemma with a female character's mother. The woman was useless, never around, never doing or saying much, just wallpaper. In the end, I just had her die while the character was young, of who knows what. (The novel takes place in the late 1700s, so it could have been anything. Even I haven't decided what killed her, the useless baggage.)
So. If he's really, really not part of the story, and his life or death makes no difference, does it matter whether he's alive or dead?
If "finding dad" is a major part of your MCs motivation or character, then it might matter. If it isn't, then don't even mention the man except in passing explanations. "Don't have a dad. Never did. He left before he knew mom was in a pickle, see, and he never gave her his address. She doesn't even remember his last name."
Course that won't work if you're a romatic. But it's more realistic than you might suppose.
Just don't get hung up on something like this for your character, if it truly doesn't matter to the story. Introducing "Dad" for the sake of your own emotional satisfaction won't necessarily make good reading. Unless, of course, you write scripts for Lifetime Television?