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Why doesn't my website appear in Google?

Google won't automatically see your website. You may need to create a Webmaster account with them for this purpose. This isn't something that Digital Pacific provides or can support, however there are guides on doing this, for example: https://blog.kissmetrics.com/beginners-guide-to-google-webmaster-tools/

There's also a WordPress specific guide here: http://www.wpbeginner.com/wordpress-seo/