It would be one of two scenarios:

The first is a sort of dark scenario where the league of villains have captured both Izuku and Momo, imprisoning them both in a unknown location (I like to believe a far off island. Which can only be accessed by Kurogiri) with quirk-dampening power collars on them both. They have no interaction outside of each other and have no sense time so they fear for the worst after two weeks (What feels like a month to them) so they finally stop and just sit next to each other watching the sunset. Momo asks Izuku at the end of everyday “Do you think they’ll find us?” and every time Izuku reassures her with “Yeah… I’m sure they will,” but at that moment he says “I don’t know…”.

After that they just start talking about their lives to each other. What they’ve done, the people they’ve met… the futures they had planned.

Izuku would hear Momo as she talked about the pressure her family would put on her as a child because of her status. And Momo listened to Izuku’s story from being a quirkless nobody bullied relentlessly to All Might’s successor.

As the month and a half point rolls around they accept Island life is all there is and they just make a routine out of it. And day by day after they accepted that fact they begin to grow closer romantically and begin to cherish each other not because they’re all they have now but because they actually mean everything to each other. After weeks, maybe months, they get brought back to civilisation and are distraught because they don’t know how to interact with anyone who isn’t them.

The other is a more light hearted situation where the whole class set up a day to go into the city and hang out. But as the day draws near each of them start cancelling one by one because of unforeseen circumstances. The only ones left are Izuku, Momo, Mina, Kaminari, Kirishima and Hagakure. But as a joke Mina says that all of them should cancel so that it’s just Izuku and Momo but tells Hagakure to tell them to cancel as well; but of course she forgets to do that so Izuku and Momo go anyway. Of course it’s a little awkward but as they realise it’s only them they decide that they might as well enjoy the day together. First it starts as two friends enjoying a day out but as they begin to joke and laugh with each other, then it slowly becomes more and more like a date with each passing minute. By the end of it they’re holding hands with the occasional bit of awkward flirting.

Mina was quickly shocked that three weeks later that the two of them were officially dating and had gone on a few more dates since then.