Chase usually reports in a few weeks, from my experience with them. Usually I call and ask when my billing cycle will end, and a few days later it should post on your CR.
First statement, or possibly the first time you pay it down to a zero balance.
That is one interesting 'feature' with the Chase Amazon card, that it lets you force extra reports to the CRA when you pay the balance to zero. Although, how quickly you will see the effect in scoring or alert updates can vary significantly.