Assuming it will be bottled (which most beers for beer club will be), a typical kit will spend 14 days fermenting, 2-3 days in the bottling bucket, a week warm conditioning and then a minimum of four weeks cold conditioning before it even becomes drinkable. That's 7-8 weeks from brewing. Kit beers taste even better when allowed to condition for 6-12 weeks so that'as anything up to four months.
As I wibbled earlier this year, I've been making lager which requires a three week lagering (obviously) period between fermenting and bottling and it then requires the full 12 weeks conditioning. The Brewferm Gold I brewed first thing this year is unlikely to be ready until mid May at the earliest. Not only does it take an age to be ready but it ties up a fermenter for five weeks. These days I have four FV's (fermenting vessels); two standard fermenters, one bottling bucket (fermenting vessel with little bottler attached) and a wine fermenter which doubles as another bottling bucket and a cider fermenter.
I've released my inner nerd and knocked up a spreadsheet which enables me to schedule my brewing and maximise my productivity but it is still only going to give me drinking beer mid May. I seems my options are either to buy a fifth fermenter so that I can double production in the short term or to invest in a 10 gallon all grain set up which finances dictate will probably occur in September. I've just put a request on my local Freecycle/Freegle board and we'll see what happens but an extra fermenter looks like the only option in the short term. Running out of beer would be, frankly, disastrous.