Last year was the first time with my 10 yr old. Went to the Amphur and got the official letter, had copies of mother's passport and DL. Nobody asked for anything. This year was our second trip and didn't bother with new letter.
As a side note here. Last year I went through the Thai passport holder immigration with my kid at BKK. This year leaving BKK, they have a new system where only a Thai passport holder can be processed in the Thai line. The passport is scanned with no IO, I had to drop out of line and get with the foreigners. If the kid is way young, could be an issue.
Now coming back to Thailand I was able to follow the kid through the Thai passport holder line as an IO processed the thai passports in person.