Yes, it is important to submit your sitemap to Google Search Console as it helps Google recognize, crawl and index your website faster. If you fail to submit your sitemap to Google Search Console and Bing Webmaster then it will take time for your newly published content to be recognized and crawled by search engines.
Most Content Management Systems (CMS) like WordPress, Drupal, Joomla, Wix, Squarespace have free extensions or plugins that you can install on your website for automatic sitemap generation and update.