Simply building a website does not guarantee placement in search engines such as Google. You have to let them know you are there. Google does crawl the web looking for new sites to add, but waiting on it to find you can literally take months.
You may want to sign up with Google's free Webmaster tools. This is a set of tools and tutorials for webmasters to use to let Google know their sites are up and running. Google will confirm the site's existence and then index it.
I hope this answers your question. If you have any more questions or information specific to the issue please leave a comment below so we can further assist you.
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