So your program starts in May and you traveling in June, does not make sense. And you have more chance of winning the lottery than getting your study permit in one month
Due to covid, this is a normal scenario, many people are doing their course online and waiting for a study permit so they can go, but it is only applicable if the semester is 100% online.
Starting march, what I observed that people are getting their study permit within a month, IRCC is decreasing their processing time.