I believe your card was approved in August (you should have receive an SMS from UOB, and then subsequently receive the physical card in your letterbox about 1 week later).
The month your card was approved is the month where the quarter starts. So 1st quarter is Aug, Sep, Oct. The statement date/cycle is assigned by the bank so since you mentioned yours is 2nd of each month, the first statement cycle is until 2nd Sep.
For the 2nd quarter, the first statement cycle should be from 3rd Nov to 2nd Dec, second statement cycle from 3rd Dec to 2nd Jan, third statement cycle from 3rd Jan to 2nd Feb. I am only 90% certain, so maybe others can chime in.