You will enter Thailand on visa exempt scheme. You are going to go to IT Square Laksi Plaza temporary office, just next to Lak Si station of SRT Dark Red Line. That is the only office you can apply for your tourism extension in Bangkok.
30 days of Tourism extension would be added to your stamp, there is no downside to going there to apply earlier. You can go anytime you want, even can go there straight from the arriving airport.
See attached for general information.
You will go here.
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And you can book online here
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