Started a new character the other day. Turns out that you can, carefully, get a low-level character to The Pitt. Got her there at level five. I remember Sniffles saying that she or her significant other got there at level two.
Anyway: picture here. No thumbnail, sorry. She's wearing some armor acquired in The Pitt.
The reason for me going to The Pitt early on is that it is a relatively easy way for a new character to get some nice gear and a decent amount of ammo & stimpaks. The only real difficult part for me was the sniper on the bridge.