Ask any SEO agency who has been in the SEO industry for any amount of time and they will tell you that ranking a site on Google's first page can take anywhere from 1 month to 6 months depending on a number of different factors.
For example, if you have an established website then it can take just a few weeks for your SEO campaign to kick in if there is limited competition.
On the other hand, if you have a new domain that isn't out of the Google sandbox yet, or if you are competing for a high volume, high difficulty keyword or phrase then it can take 6 months or more. (Using the services of an SEO consultant during the build process of a new website is generally a good move.)
It is important to appreciate that SEO is a long term investment; albeit an investment that will reduce your reliance on advertising in the years to come.
If you'd like a trusted SEO Consultant to take a look at your site and give you an estimate on how long is should take to rank then get in touch today.