Admission Confirmation Timeline after results are released

Hello,

I received my A Level results on the 11th if August and an placing to travel to the USA on the 21st, and will travel to Canada from there. I was wondering if I will receive my admission confirmation by then. I had the results sent to the university directly from Cambridge as soon as they were released via the priority results option. If anyone has experienced this can you tell me how long they usually take to clear the conditions? I did need my requirements. Thank you!