After you submit your application. Like it or not, after you submit your application, the ball is in the employer's court. They might not even be reviewing applications for a few weeks, or they might have hundreds to sift through. So this stage of the game is about being patient.
Job seekers are sometimes advised that they should call at this stage to "check on their application" or to try to schedule an interview. But most employers don't respond well to this, viewing it as overly aggressive and, yes, annoying. After all, you're not the only person applying for the job; multiply your phone call by 200 to 300 applicants, and you'll see why employers are annoyed.
Realistically, the way to stand out at this stage isn't by having an overly aggressive, rules-don't-apply-to-me, pay-attention-to-me-now approach. Instead, you'll stand out by being a highly qualified candidate, writing a great cover letter, and being responsive, thoughtful, and enthusiastic.