It won’t show up immediately on Google due to its sandbox feature — i.e. a test period in which Google want’s to ensure that a new website is not a search-engine trap. i.e. that as soon as it’s index it will change all its contents. We don’t know much about the details of how Google handles the whole process, but I remember when the sandbox feature first came out (a couple of decades ago) to counter the above mentioned practice (e.g. waiting for a site to be indexed for some given keywords, and then switch to different contents, often counterproductive to the keywords for which it appeared).
Before the sandbox era, you could pretty much count on your website showing up at specific dates (beginning of upcoming month) once it was crawled. Now it’s a matter of waiting, and only those at Google know how it works and how long you need to wait.
Usually, a couple of weeks should be enough for a new website to show up in search engines, a month at the most.