Every adoption is treated as an individual case, so while the process normally takes about a week, it can be shorter or longer depending on a number of factors, and this typical timeframe should not be taken as a guarantee.
Occasionally cats might need to get to know their new owners more gradually over several visits and others might be completing veterinary treatment before they can be adopted.
If you know there is a big event (moving house, going on holiday, a new baby) coming up soon, it’s best to start the process after everything has settled down, so that whenever you find your new cat, you’re ready for them.