You can apply for a 60 day visa from the Thai embassy in America or you can get a 30 day visa exemption stamp on arrival in Thailand. Either are eligible for a single 30 day extension at an immigration office inside Thailand for a fee of 1900 baht.
Based on you trying to move to Thailand and transfer to a retirement visa I would suggest you get the 60 day visa just to be sure you have lots of time.
every office will seem to apply some variant of the rules, but you do not need to have any number of reports done before you can request a residency certificate. We got our first one while on a tourist visa after less than a week after arriving.
You will need a copy of your TM30 though and a passport photo, along with a copy of you passport and a copy of the page(s) in your passport with your visa.