You have a platform available to you here within WA, and one that allows you to track your rankings over time.

Go to the Research => SiteRank

This will allow you to see where you are ranked in Google, Bing and Yahoo for particular keywords, for any website that you want. You can even track the competition.

You may check out Site Rank in Jaaxy.

You may input your keyword and domain name.

First your posts get indexed and often days later down the line start getting noticed provided targeted keywords are searchable, new websites can rank efficiently.

But typically "authority" for a website starts to get established through time, usually the 3-6 month mark.

They fluctuate up and down the scale till Google decides where to place them.

Not all posts will get ranked, thus the recommendation to keep updating blog 2 - 3 posts a week and that's for the foreseeable future.

https://my.jaaxy.com/siterank/search

You may also like to review Kyle's resource
. 4 Things You Need to Understand About Your SEO Rankings