1. Check whether you are in the index at all
Type site:yourdomain.com into Google. If nothing comes back, the site is not indexed and no SEO means anything until that is fixed. The usual causes are a new domain Google has not crawled yet, a robots.txt blocking access, or a noindex tag left over from the build. The last one is the nastiest, because the site looks perfect and is invisible. Register for Google Search Console, because without it you are guessing instead of looking.
2. Search for yourself the way customers search
If the site appears for your business name but not for the service, the site is indexed and everything works: you simply do not rank for competitive queries. That is not a fault, it is a lack of authority and content. A business name is an easy query because nobody else competes for it.
3. Local queries read the profile, not the site
For "near me" searches and for the map, Google shows the Business Profile. Without a profile you are not on Maps, and the website has nothing to do with it. If the profile exists but does not appear, check that it is verified and not suspended: Google announces suspensions by email, which often lands in promotions. The setup guide is here.
4. You see yourself, but others do not
Google personalises results by history and location, so you see your own site far more than anyone else does. Check in a private window, or better, ask someone in another city. Rankings are not measured by searching for yourself but in Search Console, which records how often you were actually shown.
5. Sometimes the answer is just time
A new domain needs weeks to months to enter serious results, and three to six months is normal for competitive queries. If the site is two weeks old, nothing is broken. What speeds it up is not a trick but steady work: pages that answer real questions and mentions from other sites.