Nope, that does not include epic feats. Epic feats are not just feats, they are epic feats.
Exceptions have to specifically allow epic feats. Without the term 'epic' there, that's not given.
Same as you cannot pick epic fighter feats when you gain levels in nonepic fighter, although you can select fighter feats and epic fighter feats also have 'fighter feats' in their name.
If you do not accept the above-quoted limitation for gaining epic feats, then everyone can simply pick up epic feats even at nonepic levels.
How about Blinding Speed, all you need is Dex 25 to qualify, or Damage Reduction, which has only Con 21 as a prerequisite. Dire Charge is also good, a fighter can have that at 1st level already with the mere prerequisite of Improved Initiative!
There's no general rule, which says, that you can gain epic feats only after 20th level.
There is a general rule, which says, that you can only gain epic feats from the bonus feats every three levels, starting at 21st, and from the bonus feats gained from epic classes, though. This is the limitation, which disallows these feats to be taken before epic levels are reached, because only some bonus feats can be used to gain epic feats, and those happen to be impossible to obtain before 21st level.
Bye
Thanee