How can I extend my Non-O Visa stamp if I need more time to gather requirements?

Assuming you got married in the US you need to get your marriage certificate apostilled by the relevant authority in the US. There are services that can get it done in 72 hours, but it then also needs authenticated by the Thai embassy in the US. Once in Thailand you need to get it translated into Thai and approved by the MFA before taking it to your Amphur to get the certificate you need for your extension of stay

That marriage cert is going to need a state certification, a US State Department certification and a stamp and signature from the Thai embassy or Consulate serving your area. Then translation and a stamp from the Thai Foreign Affairs dept befire you can use it for your Non-0.