If the narrative is in past tense, you could relay the notion that the narrator learned the extra information after the fact, and chooses to tell it at the points when it is relevant, despite the fact s/he could not have been there at the time.
Of course, I'm of the opinion that if you want a 1st-omni narrator, then go for it. My least favorite college professor tried to say that 2nd person narrative was impossible. Nothing's @#$#ing impossible, we're writers! If disbelief couldn't be suspended we'd all be wasting our time! I write to immerse myself in something that I can't have in my own life. If every word I wrote had to be something factual or possible, I'd hang up my pen and never write again.
I'm not saying 1st omni or 2nd is easy, and certainly they aren't common. But if it's what you want for your story, you find a way to make it work.
Edit: I apologize if I came on a bit strong here, but I swear, this one professor's limited, 'my word is law' viewpoint on writing just gave me a twitchy reaction to being told something can't be done. I thank the AW community for being much more reasonable than her.