As vangogh said, you can be #1 for a non-competitive phrase as long as your page is included in the index. This depends on the number of incoming links you have. That's as easy.
From my experience, I can say that 5-12 hours is enough, mostly. A high traffic site will do it even faster.
However, I don't see a point in clocking the time to get indexed. Quality is what matters
Not to mention you need to
optimize your site for the humans anyway.