Timeline of application

Good question! There's 3 key things that come to mind when considering timing:

• Strong CV: Is there anything going to happen between now and May, let's say, that will make your application stand out more? If you're an undergrad with no work experience, an internship will look good! Hence, if you have planned one, you might want to hold out to make this particular experience shine
• Referrals: Are you getting support from firm members? Applications are strongest when you're being referred internally. This requires networking and relationship building and doesn't happen overnight.
• Interview practice: Do you have a baseline for your case/personal fit interview performance? If you're at 0, I would hold out just a little bit. The idea is to get some practice and better judge what it takes to get to 99%. This is hard to tell when you're a complete novice.

Generally speaking, consulting firms recruit on a rolling basis (apart from campus recruitment for internships or similar). Hence, it makes no difference to them whether you apply now and agree on a schedule where you'd be starting to interview in 3 months.

However, if you're unsure about any of those 3 points above, I would hold out a little. There's no rush and nothing to gain from being early. Assume that, unless you specifically ask for time, approximately 4 weeks will pass between application and first interview round, should you be invited.

Hope this helps! Best of luck and let me know if you need help with anything in particular!