Depending on how you applied (via a program, referral, etc.), the role, and their current demand, you can expect a response as soon as 1 week or even as long as a few months.
Unfortunately, yes this is a wide range of time! Your best bet is to reach out to any contact you have in BCG and/or try to reach out to HR in a few week's time.
I would also highly recommend that you commence case prep now in anticipation of being invited to interview - by the time you find out you're interviewing it's normally too late!