Brand New domain name (never used before) needs 3 to 12 months to be well known by the search engines.
Make sure that your domain name is not blacklisted for any reason that prevent indexing your links.
Verify your Server IP address using trusted authority websites and Dns checker, if the IP is blacklisted or not.
Build the confidense between you and Google by verifying your website ownership by installing a code to your head section.
Connect your website with Google search console and Google analytics, to use all google free index and tracking services.
Build the confidense between you and Bing by verifying your website ownership and installing a code to your head section.
Connect your website with Bing webmaster, to use all bing free keywords research, index and tracking services.
Highlt recommended for Any business with a phisical address to create your business profile on Google and Bing.
Create a Pro links and images google sitemap xml and submit it to Google/bing. Its free.
Generate a pro meta tags content for every page. including title, description and keywords. and avoid duplication.
Create a correct open-graph for google, facebook, twitter, onevery page of your website.
Make sure that your website is responsive and mobile friendly, to appear on mobile phones.
No need to be a Seo person to do some basic optimization on every page of your website.
Compress, resize and optimize all my images. to help your page to load fast. Convert images to Webp format is a plus.
Check for missing images atribute. to get more chances to appear on images search engines.
Check for broken links on every page of your website, and fix it or remove it, to avoid unindexing links.
Create a 404 page with more links and information to go back to the homepage. This also increase your website hits.
Very important to create a htaccess and robots txt if it doesn't exist. To control the access to your site.