It is possible to renew without an appointment. You can line up before the official US passport office opens, and they have a line for those with appointments and those without. I would plan to go a few days in a row if possible. I live in a large city so I didn't mind possibly going a few mornings, but I got in my first try. The people at the tail end of our line didn't. Maybe 20 got in, and 10 didn't that day. I was #3.
A bunch of us were there 2 hours before the office opened (**check the hours, diff opening times on diff days). The guards are used to folks waiting (this must happen often) and they just told us where to wait, estimated time for us, etc. Folks with appointments started to line up. After a while, they started letting the non-appt folks in. More lines inside, but once I got to talk to my person, they said to come back in 2 days and that was it. I had I think 5 days before my trip. The guy next to me in line drove for 6 hours to get here, so they gave him his passport that day. That's fair. It was easy for me to come back in a few days, much harder for him.
What you must do is have all of your paperwork done, signed, ready to rock. If not, you have to work on it there and that looked painful. I don't know what happens to your place in line. I printed all my stuff ahead of time and was ready. It was about a 3 minute discussion once I got to my person. Picking up was fast too: walk in, show ID and boom ya done.