The best thing you can do is make sure that your mortgage rep is staying in touch with the underwriting division of his bank. A good mortgage rep will have made friendships with one or more people in the company's underwriting department that he can keep in constant contact with and hopefully they will treat him favorably while your loan request is being considered.
Aside from that, there is nothing you can do other than submitting all documents requested as quickly as possible.
Since your mortgage broker did not give you a underwritten preapproval there can be plenty of questions the underwritter can have. Any deposits over $1000 that isn't from your paycheck is questioned. Your credit report is checked to make sure you are you. They look at employment and addresses on it. Any credit card you use is going to have the current minimum payment included in your DTI.
Underwritting takes 2-5 business days depending on the work load of the lender. Expect a commitment asking for more items then you gave, that is normal. Good luck!