We would like to recommend you to follow the points covered below to increase your brand credibility in Google search engine result.
First, you should figure out the right keywords based on your business model and defined the buyer persona.
To identify the right keyword for your business, you can use the tools like Ahref, UberSuggest Keyword research tool or Google Adwords keyword planner.
Based on your researched keyword, write compelling content to attract prospects for your business.
Contact with influencers who can publish or share your content, but must ensure that the followers are influencers on your website .
The content of your blog should be well written based on your customer's pain point and should satisfy their intent of visiting your site.
On social media channels, let join in communities based on your business and should share your content or blog with them highlighting the service.
Such an approach will definitely acquire qualified traffic to your website and will also enhance your brand credibility among locally targeted customers.