Working through the causes.
FIRST, CHECK WHETHER IT IS INDEXED
Search for your exact domain name. If nothing appears, it is not indexed.
Use Search Console's URL inspection on your homepage, which states whether it is indexed and why not.
THE COMMON CAUSES
The WordPress setting discouraging search engines, left enabled from development. Settings > Reading. A noindex tag in the page source robots.txt disallowing everything The site is too new, and has not been crawled yet No sitemap submitted and no links pointing at the site The site requires login or is password protected
CHECKING QUICKLY
Visit yourdomain.com/robots.txt and read it View your homepage source and search for "noindex" Check the WordPress reading setting
Those three account for most cases.
IF NONE APPLY
Submit a sitemap, request indexing for the homepage, and wait. A genuinely new site with no links takes time to be discovered.
GETTING FOUND FASTER
Links from any existing site you control, a business profile, and social profiles all help discovery.