Bring your US marriage license to an official translator’s office in Bangkok. Ask them if they have any upcoming appointments slots to then bring their translated version to be certified at the Ministry of Foreign Affairs for you. They will get you in much faster then if you try to do it all by yourself. They don’t charge too much anyway. The translator will then collect the certified “notarized” Thai translated copy for you and you will pick it up from the translator’s office or can have it mailed to you usually. Good luck.
It needs to be translated to Thai by official translator and then you can also hire them to send it to the Ministry of Foreign Affairs to be certified. Otherwise doing it yourself can take longer. There are several translation offices in Bangkok, especially near the embassies.