I booked my first magazine tearsheets and got my first roles as a TV extra and as a lead in a music video that aired on MTV through my own persistance and submissions.
You can mail your headshot to casting directors yourself, and then you will get a call from the agency and get a time and location and you will be told to bring your Social Security Card and ID and you will be told what you wear.
I have been booked sometimes and never seen the casting director face to face.
You might never see this casting director face to face, or you might come in and meet with them, but it is normal if you don't. For background work usually it is just a certain look they need and the personal relationship between casting director and background extra does not happen.
On the other hand with a commercial print modeling agency - you will go in and meet face to face the agent. With all of my commercial print modeling agencies I have met them face to face. Because they will be sending you on more selective castings and they will want to see you in person. Which means if you change your look you would want to confront them about it.
Also by working with photographers who submit to magazines and work with commercial clients I have also gained modeling tearsheets. It is good to work with photographers who are as driven as you are!
I have also submitted myself to roles for music videos ( for example: Coheed and Cambria, Univision, My American Heart, and many more) just by my own mailings to the production studio or the electronic casting.