Can I extend a 30-day tourist visa obtained from Mae Sai border at immigration?

you don't have a 30 day tourist visa because there is no such thing :/

You have a 30 day visa exempt entry BUT be that as it may, you can indeed go to the immigration office and get a 30 day extension for 1900baht

You need a copy of the data page of your passport, the entry stamp, your departure card, a passport sized photo and the filled out TM.7 application form