Is there a specific waiting period to extend a 30-day visa in Thailand?

What immigration office will you be using ?

at most offices you can apply for a 30 day extension when you have 30 days or less left on your current stamp (so in theory you could go right after getting out of the test&go hotel)

BUT

In Pattaya at Jomtien they will tell you to come back when you have less than a week left on your current stamp SO it varies office by office.

I've always done it a week after I'm in Thailand and never had an issue. Wishing you the same.