You can get a Residence Certificate from your provincial Immigration Office for free. However some Immigration Offices (like the one in SiSaKet province) only provide it when you have a 'request form' from the DTP that provides Thai driver permits. If that is the case also in the province where you are residing, you should first go the DTP where you plan to apply for the Thai drivers permit, and ask them to provide you with such a Residence Certificate request form (it's free of charge). And with that request form you can get the Residence Certificate from your provincial Immigration Office (free of charge). Then it's back to the DTP to do the actual application for your Thai drivers permit.
Last month I went through the process, and I had my 2 Thai drivers permits (one for a car, and one for a motorcycle) provided in less than 1 hour, and it cost me 320,- THB in total.
All I had to show was:
- My Passport with valid permission to stay (and two pass-photos)
- The Residence Certificate
- A 'health' certificate less than 1 month old (which you can get at most local clinics for 60,- THB)
- My non-expired International Drivers Permit
However, you will not be able to do that, as you do not have a valid International Drivers Permit or - in case your drivers permit is not in english - an Embassy stamped translation of your country's valid drivers permit. So you will have to go through the whole process of proving - both theoretically and practically - that you are able to drive a car/motorcycle.