Before he met Finn, Poe slept around a little bit. Of course he calms down when he meets Finn and they become a couple, but one day a lady turns up holding a baby that she is adamant is Poe's, and well. He can't deny that it has his eyes and hair and, okay, yeah, that baby is definitely his.
Cue Poe having a crisis about suddenly becoming a dad, Finn being supportive and enthusiastic about it (he never had the chance to be around babies and he's really excited to have the chance to be around a child of Poe's especially) and the two of them struggling to figure out exactly how one takes care of a baby when its mother leaves the baby with Poe.
+ Poe not instantly being an amazing father. He tries his best but he's already overworked and getting up to feed a crying baby several times a night is draining/frustrating.
++ BB8 is jealous at first but comes to be a baby whisperer of sorts and can stop baby crying with the right combination of beeps and spins and light flashes.
Finn/Poe, Poe gets a surprise baby
Cue Poe having a crisis about suddenly becoming a dad, Finn being supportive and enthusiastic about it (he never had the chance to be around babies and he's really excited to have the chance to be around a child of Poe's especially) and the two of them struggling to figure out exactly how one takes care of a baby when its mother leaves the baby with Poe.
+ Poe not instantly being an amazing father. He tries his best but he's already overworked and getting up to feed a crying baby several times a night is draining/frustrating.
++ BB8 is jealous at first but comes to be a baby whisperer of sorts and can stop baby crying with the right combination of beeps and spins and light flashes.