Hi Marcus, as an agent and a landlord, I can tell you the verification process may vary greatly. Some places require more than others, and this may take more time. Others require very little and you may move in next day, especially private rentals. At the worst, rent a weekly for the time it takes to process your documentation.
If you wanted to get started right away, and have all of the necessary documentation, it may be possible to find you a place by the weekend. Let me know if I can be of service.