To move into a big 4 Audit role specifically there are two options. First you can be part of a graduating class from either a Bachelors or Masters program and enter as a first year associate. Second, you can apply as an experienced associate from a smaller firm by which an employee referal would be very helpful...

From what you stated above it doesn't seem that you would fit either examples. Your best bet would be to try to land an entry level job at a smaller firm and apply after one year. Depending on your area its not very hard to get an offer in this situation. Im in the northeast and my big 4 firm has brought in so many experienced hires from smaller firms I wonder if they now outnumber those who started their career here... This also has to do with the incredible turnover in the first two years I suppose...

Thats really your only option unless you could convince them your experience in statistics related to another branch of assurance like systems processing, IT, or risk assurance... something along those lines. Unfortunately I can't answer any questions about those groups...