This is my first PCS. How long after arriving at my new duty station will it take to recieve my BAH so i can pay the security deposit/rent?

If there are no issues, right away.
But for a PCS you also qualify for DLA and you can take out a loan of one months base pay that you pay back over 12 months interest free.
Always a good way to pay down car payments, credit cards, or anything you are paying interest on now.

You will continue receiving BAH for you last duty location until you complete your inprocessing at your new location. It has taken me anywhere from a couple weeks to a month for the BAH to adjust after inprocessing. Bear in mind that it may take longer now due to Covid...

Your geographic location will be updated when you check into IPAC. The date will be back dated for the day stamped on your orders. your BAH should be updated for the next pay period. You can request TLA to assist with reimbursement for temporary living arrangements while you locate a residence. Advanced Dislocation allowance requested when you complete your outbound interview in MOL and with IPAC is the best way to pay for your deposit.