We don't manually submit website URLs to search engines because these days search engines themselves are to the point where you don't really need to manually submit them for them to be recognized - as just by a website being live for a certain amount of time, it will automatically be indexed.
There are certain cases you'd want to submit a sitemap (or a list of all pages on your site including the main URL) to Google for these reasons (taken right from https://support.google.com/webmasters/answer/156184):
- Your site is really large. As a result, it’s more likely Google web crawlers might overlook crawling some of your new or recently updated pages.
- Your site has a large archive of content pages that are isolated or well not linked to each other. If you site pages do not naturally reference each other, you can list them in a sitemap to ensure that Google does not overlook some of your pages.
- Your site is new and has few external links to it. Googlebot and other web crawlers crawl the web by following links from one page to another. As a result, Google might not discover your pages if no other sites link to them.
- Your site uses rich media content, is shown in Google News, or uses other sitemaps-compatible annotations. Google can take additional information from sitemaps into account for search, where appropriate.
We do have a plugin installed on all of our clients' sites that helps with basic SEO optimizations and also generates a sitemap that can be used to submit to search engines through Google Search Console (formerly called Google Webmaster Tools, and it is a separate service that has to be signed up for with a Google Analytics account).
We can help you with this if you strongly prefer it to be submitted.