If you don't buy a tourist visa from the thai consulate in the US before you wing your way here, you're only gonna be here for 15 days on the Visa On Arrival that you buy when you land and go to stamp in here 😮
Sadly being a permanent resident of the US doesn't cut any ice getting in to thailand 😕
BUT
it would let you use the eVisa site that the thai consulates in the US all use so you could apply for a tourist visa online
***************************
Make a profile, log in, etc and apply for a single entry tourist visa at the thai consulate based on where you are in the US.
It's all done online, they will email you the visa as a PDF that you print out and give with your passport when you stamp in. You will get stamped in for 60 days and you can extend that one time for 30 more days at the immigration office where you stay for 1900baht after you're here