Entries to FA Cup Competitions are optional, and clubs pay an entry fee.
However, to play in the FA Cup (which everyone wants to play in), you have to play in the FA Trophy/FA Vase (or be a Football League/Premier League member) the season before.
You have to go back to 2008 (before today) to find the last winners of the FA Trophy who aren't an ex-League club. In fact 3 of the 6 are in the League now!