I've moved multiple times while very broke (running around trying to find a cash machine that would dispense $5 bills, eating out of a frisbee until I could afford plates broke, on several occasions). I had enough for the deposit and first month's rent, but had to wait to afford much else.
For setup costs, you can do it surprisingly cheaply if you lower your standards and don't regard things like a bed frame or drawers as necessities. A cheap single mattress on the floor works as a bed plus couch. A cheap bed in a bag, a towel and washcloth, and a few dishclothes for linens, a small card table and folding chair for a desk/table, and a set of no frills assemble yourself shelves from Walmart to store stuff on will do it. Toss in an iron if you need one to look respectable for work (ironing board not needed - iron on the bed). Cardboard boxes can be fashioned into bedside tables, dresser drawers and bookshelves.
For a kitchen - you can get by at first with one cheap pot and a cheap frying pan, a plate/bowl/mug/knife/fork/spoon, a cutting board, a paring knife, a vegetable peeler, a colander, a mixing bowl and a mixing spoon and spatula. Most of these things could be purchased at a thrift store. Start up food can be very basic - a bottle of oil for frying, salt and pepper, a couple of cheap spice mixes, maybe a bottle of soy sauce and of vinegar, and you can cook enough to keep yourself fed and healthy without a big initial outlay for ingredients.
Once you've got the above, and some basic cleaning supplies, you've got enough to survive on. You can upgrade and add things as you go.
It's not luxury living by any means, and I'm glad I'm no longer having to do that any more, but if you really want to move out as soon as possible, it can help to calibrate your options - moving into a nicely furnished and equipped apartment is nice, but not required.