It depends on how hard you work at your website and get traffic.
Some can start making good money with their website in just 2 years while some may take a decade or longer.
If you expect to make a living from blogging you'll need to make sure you consistently add new blog posts at least 3 times per week.
You can't just blog once a month and expect to roll in the traffic and money.
Google favors websites that have constantly updated and unique quality content.
And the more blog content you have the more chances at your blog being found in google search for keywords.
Do keyword research also and focus on long tail keywords that are much more easier to rank for.