Enough for the client to draft a scope document and for the experience evidence to be assembled. The scope document is the slow item because it usually needs revision, and former employers are slow to produce dated letters.
Short engagements need long lead times
Hypothetical example: a Hampton consultant is asked to start a ten-week engagement in three weeks' time. The compressed part is not the application; it is everything that has to exist before the application makes sense. The client's first draft of the scope will usually describe a role rather than an engagement and will need to be rewritten, which takes a round of comments through their counsel.
If the applicant is relying on five years of experience rather than a degree, letters from former employers and clients have to be requested, and people take weeks to respond to that kind of request. The practical answer is to keep a standing evidence pack current, refreshed after each engagement, so that only the scope document has to be produced when a short assignment appears.