The problem with Balmung is it is a 'Legacy' server that was one of the servers for the original version of FFXIV (version 1.0), and back then, it had been designated by players as the 'unofficial role-play server', thus it's always had a very large population and this didn't change going into ARR it's only increased in popularity.

Unfortunately because of this abnormal popularity, it makes inviting new people to play on it very difficult - but it is possible, you just have to try creating a character during it's quiet time (in the early morning specifically when a lot of players are in bed and only the night owls like me are still playing ), as it's often restricted during peak times.