My OPT expires March 10th, can i apply for h1 before/after expiration?

My OPT is going to expire March 10th and my emoployer is willing to finance my H1B visa, i have about two weeks before OPT expires. What are my options? Can i apply for H1B before or after expiration date?(does it matter?) I know i’m not goting to be able to work after expiration date but can i work after i apply for H1B before it is approved or denied? And i’m not eligable to apply for STEM exptension because i only have assoiate degree from USA and Bachelors from my home country. I received my OPT after completing 2 year associate degree. What are my options here do i have to go back home and come back to USA in october 1st ?(If my employer is still willing to wait for me and don’t fill the position i’m working now)

Thank you for help.

You will have a grace period of 60 days (i.e. up to around May 10) to stay in USA after your OPT expires. So you can apply H1 on April 1st which is when USCIS starts accepting H1 applications but you cannot work from March 11th to Oct 1st . H1 authorizes you to start working from Oct 1st only. Therefore, applying H1 on April 1st 2013 will only help you to legally stay in USA till you hear the decision of your visa/Oct 1st but DOES NOT allow you to work during that period.