Google does need some time to make sure the site is indexed and appearing in their searches. This process can vary anywhere in between a week or two and 6 months but the previous case is certainly the more common one.
There are also ways you can speed up the indexing by manually submitting your site to Google.
If you have a Gmail account, you can open this link: https://search.google.com/search-console/about (https://search.google.com/search-console/about) and follow the steps explained here:
https://www.youtube.com/watch?v=RCb0rD1n2Yc
Hope this helps!
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