Do you need a Sitemap?

From Google’s knowledge base.

Do I need a sitemap?

If your site’s pages are properly linked, our web crawlers can usually discover most of your site. Even so, a sitemap can improve the crawling of your site, particularly if your site meets one of the following criteria:

• 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.

https://support.google.com/webmasters/answer/156184?hl=en

Another important thing to note from Google’s documentation is this:

Using a sitemap doesn't guarantee that all the items in your sitemap will be crawled and indexed, as Google processes rely on complex algorithms to schedule crawling. However, in most cases, your site will benefit from having a sitemap, and you'll never be penalized for having one.