A clarification worth mentioning in regards to the currently accepted answer is that the age of a page does matter, but search engines do not automatically use the written copyright date to influence how old it thinks the page is.
Search engines crawl pages on a regular basis looking for changes; so, if a page has a copyright date of 2010, but was last modified a week ago, they can tell that the content is more up-to-date than a website with a copyright date of 2021 that has in fact not been updated since 2021.
That said, publication dates can be passed to Google in such a way that can influence search results. While not really necessary on all kinds of websites, if you run a site where it is important to prioritize your newest posts or make your content searchable by date, then you should include both a visual publication date on your page and specify it in your page's structured data, and as long as you did not mark a future date, Google will take this date into account when prioritizing its relevance.
https://developers.google.com/search/docs/advanced/appearance/publication-dates