Short answer
Google says “crawling can take anywhere from a few days to a few weeks.” That is only to be found and indexed. Ranking well for competitive searches usually takes much longer, and nobody can guarantee it.Getting indexed: days to weeks
Before a site can appear at all, Google has to discover it, crawl it and add it to its index. In Google's words: “Crawling can take anywhere from a few days to a few weeks” ( Google Search Central).
What helps:
- Add the site to Google Search Console and submit your sitemap.
- Use URL Inspection to request indexing of your most important pages.
- Get the site linked from somewhere Google already visits: your Google Business Profile, directories, social profiles.
Don't keep re-requesting. Google notes that “requesting a recrawl multiple times for the same URL won't get it crawled any faster.”
Getting ranked: months, if at all
Being indexed means Google knows the page exists. Appearing near the top for a search like “accountant in [your city]” depends on how well the page matches the search, how many established competitors there are, and how much of the web vouches for you. For a new site with no links yet, that is a matter of months of steady work, not days.
Your business name usually comes first. Searching for it is the quickest way to see whether Google has picked the site up at all.
Checking progress
Search Console shows which pages are indexed and which searches you have started to appear for. A site: search is a rough check, but Google warns it “doesn't necessarily return all the URLs that are indexed” ( Google).