First, let's check if is this my website or is this Google...
Try searching for your website on Bing, Yahoo, DuckDuckGo etc if it appears then we know this is a Google issue.
Let's check if the site has been indexed by searching on Google site:yourwebsite.com. if it appears then let's check some of the below.
This isn't a site issue as it's being picked up on other search engines fine and when checking specifically the site google has indexed it. This is Google not ranking the site high enough to display on organic searches. Some things you could do that may help:
Set up Google places
Set up Google Analytics https://help.reffle.co/en/articles/11417164-how-to-set-up-google-analytics
Set up Google search console https://help.reffle.co/en/articles/11426962-how-to-verify-your-site-with-google-search-console
Make sure Google Places, companies house and contact us addresses all match identical
Ensure some real organic backlink traffic goes to the site. (traffic from other sites)
Google ads on the site may help
I would caution that we rarely see any traffic to competition sites coming from Google it's all from social media where the focus on growth should be.