Akira's a good one (Movie) BeBop is a must watch (Series, 28ep iirc) Perfect Blue absolute banger (Movie)
These titles are pretty old, yes I know. but old != bad keep your mind open.
I'm not certain where you could find all of these titles in one place, but I am almost certain that there's an upload on yt for all of these but they usually get taken down after a few months so just look thoroughly. have fun
That aside, I really like Shinsekai yori and Monster. But those don't really fit the term "epic" imo because of their relatively slow pacing. For that you might want to try shows where Hiroyuki Sawano is responsible for the soundtrack. Chances are that those shows are going to be rather flashy. Attack on Titan, Kill la Kill and Aldnoah.Zero would be examples. Otherwise there are some classics like Fullmetal Alchemist: Brotherhood and One Piece, but those get spotted rather quickly. Wouldn't surprise anyone if you know about these shows.
Rainbow - Nisha Rokubō no Shichinin also comes to mind, but that's more gritty than epic. Also, Baccano!. It may not be considered epic per se, but it's still cool as heck. If you can handle the jumps in the storytelling, that is. Last but not least, Star Blazers: Space Battleship Yamato 2199. Could be classified as the space-faring type of epic. Cannot speak for the original series that launched some decades ago, though.
In case you want to find the right genre(s) for you, you might want to check an anime listing site and smash that random anime button until you find a cover and blurb which are intriguing. But beware: That's basically a game of risk. For an entry level watcher it would be safer to check out some anime top lists.
Oh, yeah, and Pop Team Epic. Even has Epic in its name. Is it epic? Debatable.