With millions of sites out there, Google doesn’t exactly watch to see every time a new site comes on line. You have to tell Google somehow that your site is out there.
This could come in the form of having dozens of other sites link to your site, but more often it comes from registering your site with Google, supplying a sitemap file, maybe setting up a Google Custom Search Engine page on your site, etc. In other words, do whatever it takes to draw Google’s attention.
Note that even after registering and providing a sitemap and creating a Google search page, it can still take days for Google to get to your site.
I’ve never done this, but I suppose if you were desperate, you could buy a Google ad for your site. This might shorten the time it takes to get your content to appear in Google search results, although you’d either have to come up with some dough or use one of Google’s many free ad coupons.
Whichever way you go, you’re going to have to jump through some hoops to get Google’s attention, if you’re not content to wait.