Short answer
Usually one of four things: Google hasn't found the site yet, something tells Google not to index it, Google can't reach it, or it is indexed but other pages answer the search better. Google Search Console, which is free, tells you which.First, find out which problem you have
Search Google for your exact business name. If your site comes up for that but not for “plumber in [your town]”, Google knows about you and the issue is ranking. If it doesn't come up even for your name, the issue is that Google hasn't found or isn't indexing the site.
1. Google hasn't found it yet
New sites and new pages take time. Google says crawling “can take anywhere from a few days to a few weeks” (Google Search Central). You can help by adding the site to Google Search Console and submitting a sitemap, the list of your pages.
2. Something tells Google to stay away
A noindex tag on a page, often left switched on from when the site was being built, or a robots.txt rule like this one, which blocks the whole site:
User-agent: *
Disallow: /On WordPress, check Settings → Reading for a box labelled “Discourage search engines from indexing this site”.
3. Google can't reach it
Server errors, a site that is down at the wrong moment, or a security setting refusing Google's crawler. Search Console reports these under Page indexing.
4. It's indexed, just not ranking
If Google knows the page but other businesses appear first, the work is relevance and trust: pages that clearly match what people search for, a complete Google Business Profile if you serve a local area, and other sites mentioning you. That takes longer, and nobody can promise a position.
The fastest way to get a straight answer
In Search Console, paste a page address into URL Inspection. It tells you whether that page is indexed and, if not, why. A site:yourdomain.com search gives a rough picture, but Google says it “doesn't necessarily return all the URLs that are indexed” (Google).