Yeah, it happened after manga was over, after all those years.
They were just teenagers for most of the series. You people act like you absolutely have to fall in love with the love of your life at the youngest possible age or else your love doesn't make sense. For one, Naruto and Hinata had interaction before during and after the war. There was the chuunin exams when Hinata gave Naruto that ointment and also told him the weakness to the byakugan, while Naruto said that he liked people like Hinata. There was when Hinata went against Pain for Naruto. There was when Naruto saved Hinata from those white zetsus and called her strong. There was Neji's death. There was the Last. There was the rest.
I know that even all of this may seem sparse for a couple, but there is no deadline that says that love has to happen at an early time. Therefore it is perfectly fine that they started dating after the war. Even if you don't interact for years with someone you know, some encounter or situation down the road may get you started on interacting with them more. Like I said before, there is no predetermined start time.