I'll say at least 6 months. A new website need some time to get out of sandbox!? if theres any, any time for you to create quality contents and some linking and finally google pays slow. So all adds up to ~ 6months imo.
If you are in need of some serious cash really fast, Adsense is not the way to go. It takes a significant amount if traffic to make good money off of it. The factors like ad placement, banner sizes etc can also vary the results. With Adsense, you need to experiment a lot, and that takes time. If you need quick money, I would say offer some services, do some CPA or even affiliate marketing.
it depends on the keywors you've choosen and the competition you can rank your website in less than 1 month and make more than 300$/month