Hi, in what position on google would be a site just after indexing? Is it bad if my website just after indexing is not in the first 300 on that keyword I try to optimize?
Your position on Google is... wherever Google thinks you belong whether it's in the first 300 or not. Is it bad to not be in the first 300? Well I doubt you'll get much traffic from being #300 or lower. Just one keyword? Not a keyphrase or combination of keyphrases? What are you doing to optimise the term? Onpage SEO? Linkbuilding?
If you just got indexed don't worry about the rankings yet, that won't happen for quite a while. And Lever, I like your avatar.
Instead of waiting, i would recommend you to continue with link building work to get better rankings quickly.
It is depend on which keyword you are optimize. That's not easy to get rank in first 300 if you are optimize on those hot keywords when you just get indexed. And you can get rank in 1 position if you aim on those keywords that seldom people use
It's normal for a new site to rank poorly. Start promoting the site by building backlinks as others have noted.
Once Indexing doesn't mean your website will be on 1st page... you need to do work for that like.. linkbuilding