TLDR: Starlords father in the MCU is Adam Warlock.

As I'm sure (almost) everyone in this forum knows, in the MCU Starlords father in the MCU is something old and powerful, which is why he was able to wield an infinity stone without the use of a device. Since Adam Warlock is able to wield an Infinity Stone (the Soul Gem) without any outside aid, it is not unreasonable to think any of his offspring might inherit somthing of that trait. Furthermore, according to The Know, the main antagonist in Guardians of the Galaxy 2 is Her, who is connected to Adam Warlock. Also, as stated on The Know, it would make a lot of sense for Adam Warlock to make an appearance before the Infinity Wars movies.

Here is my scenario:

1. Adam Warlock fathers Starlord and leaves him and his mother to spare them Her wrath (because if She can't have Adam no one can), or he simply was unaware of his existence until later and thought is was to late to go back.

2. She (Her) finds out about Starlord and goes to Earth (there is info out there that indicates Guardians 2 takes place at least partly on Earth) to kill his family or simply find clues as to the whereabouts of Adam Warlock and terrorizes Starlords family while doing so.

3a. Starlord goes to Earth to stop Her and runs in to Adam Warlock.

3b. Adam Warlock tells Starlord what is going on on Earth and goes there with him.

4. Starlord finds out Adam is his father.

I know this doesn't follow comic book lore but Marvel has departed from some lore specifics before.