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We appoint ambassadors in cohorts. This means once in a while we look at all the applicants and pick the users we think would be good candidates. We pick them about every 2 months. Last cohort was appointed on March 7th, so I think the next group will come somewhere in May.
So to answer your question: It depends on when you apply. If you apply 1 week before the closing date, it won't take long for your application to go through. There are also people who applied right after the last cohort was announced. They will have to wait 2-3 months.