When you have a new website, it can be quite a long time until it is indexed by google. The search bots take time to crawl over all the sites on the internet! There are some things you can do to get your site seen that bit quicker.
One of the first things you can do as a new website owner, is to manually submit your site, along with sitemaps. There are tools on the google search console (formally known as the web master tools) which allow you to manually submit your URL for google to scan.
Another key way to get your site indexed faster is to build some back links. You can do this by posting on your own blog about your site, or getting friends/family to share on their social networks. Any links leading to your site will form backlinks and are good ways to get Google to see your site quicker.