Before the banks tightened up and stopped people on free stamp (visa exempt) entries from opening bank accounts you could come here and open an account then apply for the visa in country
Nowadays we recommend getting the Non-O visa in your country before you come here, (or if you're already here go to a thai consulate in a nearby country and apply for the Non-O visa there)
Once you have a 90 day Non-O visa most banks will let you open an account
I wrote a post about it here;
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