If you come on a 60 days visa exemption or a 60 days tourist visa which both can be extended with additional 30 days is not important. You can apply for a Non O in country with both.
You’re problem is a bank account for banking the required 400K baht for Non O/extension.
As I see it you have two options;
-Just come and get married and contact an visa agent as
@THAI *****************************
who are able to assist you with opening a bank account included in assistance with the whole visa process.
- Come and get married and get all your papers, leave Thailand and apply for a Non O through an embassy in a nearby country with your bank at home to meet the financial requirements. Not a duckwalk but still possible to open a bank account in Thailand on a Non O visa and a residence certificate even though you might have to try in several branches first. Bank the 400K baht two months prior to your application for extension of stay.