Determining how long SEO will take to rank a page or article in your blog on the first page of Google depends on a number of factors.
How competitive the keyword is will be the biggest factor. Your website needs to build up authority for that keyword or phrase.
SEO for popular, very competitive keywords can take 3 to 12 months to rank in the top 3 positions, on the first page of Google. This is assuming you are starting from scratch and no SEO has been done on your site previously and your site has not had a google penalty previously.
SEO is a long term strategy, which is why it’s important you discuss your expectations at the start of any website design work.