the answer depends on the country you are considering for your application.
For entry-level roles, the usual starting dates in Europe/US are September and January. Many interviews take place in September-November (January intake) and January-March (September intake). The best period to apply as a new graduate is at the beginning of the period when interviews take place, since the process just reopened and you will have less competition. This is likely to be September for the January intake, and January for the September intake. Having said that, you should check for possible deadlines for the country interesting for you.
If you are applying via referral (strongly recommended), it would also be useful to ask the internal contact what’s the current situation in terms of recruiting – sometimes, even if in the “correct” window, there is not much recruiting due to lack of projects.
In terms of the timing to prepare, many people need to put 100+ hours in preparation, I would recommend to define a prep program and start the preparation in advance accordingly. In many cases, this means at least 3 months in advance. This of course also depends on how you prepare (quality is more important than quantity).
In terms of referrals, you can find some suggestions at the following link: https://www.preplounge.com/en/consulting-forum/hey-everyonehope-all-is-well-3176
Hope this helps,