The answer to this question depends on a lot of outside factors...
1. Domain Strength
3. Program offerings
For a brand new URL without any history Google says it will usually take 9 months-1 year to see first page ranking in its organic searches. There are things that you as the client can do to help move the process along faster (see article "What Can YOU Do To Help Your Search Ranking?"). However, depending on the 3 factors listed above, time from website launch to first page of Google results varies.
See Below Graph From Ahrefs:
If you have had a previous website provider and have had your URL for quite some time (2 years or longer), the time to optimal ranking is drastically less. However, you may take a slight drop in Google rankings when your new website launches before you climb up to the top again. This is because changing website providers and the overall structure to your site is a shock to Google, and it may take a couple of months for Google to reindex (or 're-trust) the entire site and rank the site optimally again. However, domains with a good, long history usually rank on the first page within 3-4 months of being a 97 Display live customer.