1) if you are applying as part of "fall recruiting / undergraduate recruiting for an office, interviews are likely conducted all at the same time, 2-4 weeks after applications close. Therefore, what matters is the deadline vs. the actual time of submission. If you applied 2 months before the deadline, you may have to wait 3 months to interview. (This is true for London and other offices, but may be different for some specific offices which I am not aware of).
2) If you are applying for a position being recruited year-round, interviews typicially occur 1-2 weeks after submission. However, again, this can vary. A friend of mine who applied (and got an offer) from McKinsey Italy told me the entire process took almost 6 months!!
Best way to know for sure is to contact the recruiting/HR of the office you are applying for to ask when you can expect to hear back. Instead of seeming restless, frame it as "I have other interviews/travel outside of the country planned so want to make sure it won't overlap with any potential interviews.