can i work legally for 2 month

the offer is on the way, but the company wants me to start on august 2. i don't have opt anymore. i am now holding an i-20 from a community college to keep my status.

in order to work legally from now till october 1, i must submit some paperwork. does anyone know what it is? will a letter signed by the school be ok?

please answer! really urgent! many thanks.