You can't legally get a thai bank account on visa exempt, and you'd have to already be here to get the bank account. So no, its not possible. Why people want to travel to other side of the planet without any cash in their pocket is beyond me, it's only $600 usd, so really???
You don't even bother to say what country you are from or visa type..however if coming on 60 day visa exempt you already seem to know it will be a problem... just book a camcelable round trip so you can modify your return once you get an extension... otherwise you probably in for a very miserable vacation after being denied and sent back home immediately.
The ask:thailand community, consisting of multiple Q/A groups with over 100,000 members, powers this platform. It is not an official government resource. Our members actively contribute to this resource, and while we strive for accuracy, we cannot guarantee its complete reliability. Assistance to travelers is provided as a community service.