Google will not list your site until you submit it for indexing! You can check if your site is indexed by Googling for "Site: yourdomain.com" replacing yourdomain.com with your actual domain name. If nothing appears, it's not listed and you will need to submit it as follows.
Submit your site to Google
Enter your full URL e.g. http://www.mydomain.com in the URL field. Complete any ReCaptcha fields (additional information required to distinguish between sites submitted by individuals and those automatically entered by software robots).
Click the 'Submit Request' button.