How long to SEO a keyword on top #1 Google?

How long does it take to SEO a keyword on top #1 Google?

for both cases, low, medium and high competitive keywords

Nobody can't say that, After how many days, you will get ranked on SERPs. Depend on your working style, content, competitors & Quality. But you need to wait at least 4-5 month of a new website for getting ranked in SERPs.

There is no way to give a accurate/intelligent answer based on the info you provided.

A) How well has SEO been done on your page?
Do you have a new website with your target keyword listed once, or have you preformed proper on-page SEO?
Do you have quality backlinks to your website? No back links? Spammy backlinks?

B) What keywords are you targeting?
You can build a site today, use the Fetch as Googlebot, and have it ranking #1 tommorrow for a long tail keyword like "Bob's awesome red and green sprockets"
How long it will take to rank for shorter keywords depends on how much competition there is for that keyword, and how well your competitors are performing SEO.
Ranking well for a highly competitive keyword could take months or years.

Keyword ranking is always a challenge to a webmaster. You need to be more complying to the rules of Google to get your keywords ranked faster in search engines. A good content with high end backlinks will help to improve your website rank in Google.

How long is a piece of string?

No one can predict the exact duration to get rank of a site for a keyword but involvement of Social networks boosts the process

Depends on site SEO and the keyword, links aren't as important as they once were.

It's all about content and on-site optimisation now.

Social can boost user engagement and direct traffic, so it can appear to "boost your SEO" but as SEOPub stated, is not a direct factor. You can rank a site without any social networking whatsoever and having that social interaction will not directly influence rankings at this point, though there are "social signals" that are taken into account.

The OP's question, as stated several times, cannot be answered, as there is no definitive time frame for a site to achieve rankings. It very heavily depends upon the competitiveness of the keywords, how on-page factors are optimized, and how off-page factors are optimized. There are way too many variables to provide a definite answer and anyone who tells you it takes "XX" days or months doesn't know what they're talking about.

What an interesting question, not least because unless there are people here who know the deep workings of Google, we can safely say, nobody knows. But as with all things, there are strong opinions, and sometimes empirical evidence that can provide some guidance. It seems that some sort of sites rank faster than others. If you're trying to rank a video that is hosted on Youtube, it can rank extremely quickly (at least, that's been my experience). If you have a page that is hosted on a high authority domain, that can also rank quickly (or at least it used to - my experience is 12 months out of date so all may have changed.) What seems to have stayed the same is that ordinary blog-type websites can take what seems like an age to rank. Try experimenting - measure and record what happens. Experimental evidence is worth far more than opinion. (In my opinion!)

I think you do not have to think this way. the better helpful thinking is to say what should I do to higher my website ranking position on google. for example if your website now in the result number 30 and you do some seo work and your site becomes in result number 25 - this is great job. that means your site is getting improve. one day you will find it to the top.

In general, you need to write valuable unique content, do on page seo, get relevant quality backlinks and wait until next update. usually 2 weeks up to 3 months.

Based on the competition of the keywords and the SEO methods you are using, the duration to bring a keyword to first position of Google differs. If it is a medium competition short keyword, you can bring it to the first position with in two months. However the ranking involves few hundreds of facts for Google. Right from the web design to optimizing on page, you have to initially consider optimizing the whole website for the search engine. Even if you follow all the Google policies and do effective SEO, you may not get the first position in two months. It may take three to four months. If you follow good SEO, you can guarantee the SEO position.