There is no one size fits all answer to this - lots of variables at play!
Impossible to answer.
What does your site look like? How's your competition? How are their sites? How old is yours? How old are theirs? Your vs Their backlinks? Quality of unique, content? Proper on-page seo? And on and on and on....
How long it takes to be ranked #1 on Google, it's always possible?
But a SEO expert would be able to tell after he check some things and get more info: "ok yes I can improve your google ranking of 1-2 position for sure".
Would be possible that he is able to say something like that in advance?