Commercial/Corporate Banking to Consulting

So I started my financial analyst job (analysis of credit for billion dollar corporations in a specific industry) in late May at a big 4 commercial bank (think BOA, Wells Fargo, JPM, Citi) and I've always wanted to do consulting but I didn't get an offer for a firm that I wanted to work at. I come from a good target school for consulting firms and a decent (3.65 gpa). I know MBB may be out of my range with a lower gpa, but I want to target Deloitte. Deloitte takes a lot of people from my alma mater and I really respect the company and can truly see myself working there.

Can I lateral into Deloitte with some work experience (I would be fine starting as a first year BA). Or do they only prefer college seniors? When would I apply? Do you advise me to work for a full year and then apply in order to have more significant experience and some industry expertise? Plus it would show a little more commitment?