I think books 1-6 on the whole don't fit the genre of "epic fantasy". It doesn't fit well into a single genre, beside the fact it certainly belong in the Fantasy genre in general. At its core it remains a YA growing up chronicle following the daily life of kids from 11 to 16 (most of HP could be adapted to become a "realistic" school chronicle) with unusual and fantastical events thrown-in, set in alternate/shifted universe with magic, and playing for the most part not on epic fantasy tropes but on making real with twists various tropes from (largely british) folklore about magic and wizards. It's the same source material a great deal of Fantasy uses, but Rowling didn't write in that form or with that loose core structure followed by epic fantasy (and the much older, real epics). There are certainly "epic moments", in the modern sense the word epic is bandied around to describe stuff like duels or action scenes nowadays, but the form/story is not even loosely that of an epic. From books 1 to 6, the epic is the thread woven in the background, very very slowly being readied to start.

The last book of the series is epic fantasy (despite the alternate rather than full secondary world), and it's a departure from the form and structure of the earlier series, shifting rather to that of the epic, with its long and very classical quest to get ready to face the big villain. The earlier books were preparing that epic (most epic fantasy don't even tell the readers about those formative years, the hero is thrown into the epic right away and must learn and make his way - for Harry this truly begins in book 7), but in HP they are equally important if not more than the epic story itself that conclude the series.

Of course the line is blurred in many places, as Rowling has thrown many little elements that do belong in an epic along the way, but on the whole these elements (eg: the ressurection of Voldermort in GOF, the loss of Dumbledore in HBP, Harry getting the cloak and so on) were included along storylines within books that didn't follow the form of the epic.