These are the forms for requesting the index search and then once you have the number the actual search. Doubt if you will receive the index search response in time for lower fee for the the actual search.  All of this is on the USCIS website; https://www.uscis.gov/records/genealogy/requesting-records/making-a-request-by-mail

For G-1041  https://www.uscis.gov/g-1041   https://www.uscis.gov/sites/default/files/document/forms/g-1041.pdf is the index search request  

Form G-1041A, Genealogy Records Request  https://www.uscis.gov/sites/default/files/document/forms/g-1041a.pdf is once you have the number and the form to request the actual records.

Jan Meisels Allen

Chairperson, IAJGS Public Records Access Monitoring Committee