There are a few things that you can do to improve your search results:
1. Get your free Google business listing.
2. Have friends and family check out your new website. Make sure they click around on all of the areas of the site. The more clicks the more it helps to get traffic on your site.
3. If you have a social media account like Facebook or Twitter, announce your new website and include a link for your customers and prospective customers to click on.
4. Unit Trac can help with your local organic search results, but if you are interested, look into Google Adwords Express - it's like Google Adwords, but for local businesses.
5. Use free resources like Craigslist and Facebook Marketplace to help drive customers to your site.
* Within Google Domains there are suggestions in 'Get Online with Google'. We sugggest you choose the 'Stand out on Google Search and Map'.