Are there any quick ways to level up or does it simply depend on the amount of posts that you make?
As others have posted, it depends on time and number of posts.
Activity is computed as min(number_of_posts, number_of_14_day_intervals_with_posts * 14)
However, there is a market for forum accounts - you'll often find that someone sells a full, senior, or even hero member account.
People often fear that bought accounts might be misused for shady things, but for participating in a signature campaign they might make sense (if the account isn't too expensive). But signature campaigns still require that you make regular non-spam posts, most pay per post.
Onkel Paul