That isn't possible. You need to map your old URLs to the new with redirects for SEO and user experience.
Google never forgets about old URLs, even after a decade. When you migrate to a new CMS, you need to implement the page level redirects
If there is no equivalent for some particular page you can let it 404 and Google will remove it from the index. Using "410 Gone" instead gets Google to drop the URLs from the index as soon as they are crawled without the 24 hour grace period that Google uses for "404 Not Found."
There is no directive to tell bots to forget about an old site either in search console or robots.txt.
What if you don't redirect?
It may be too much work to redirect, or your new CMS may not make the redirect implementation easy.
If you choose not to implement the redirects it will be something like starting over. Google will see that your old URLs return 404 status and it will remove them from the search index.
Your new URLs will eventually get indexed, but it may take a while. Changing all your URLs without redirects is a big sign that your site isn't stable and can't be trusted. All your rankings will be lost and your site will start over.
Googlebot will continue to crawl the old URLs for years. For it, hope springs eternal that you may someday put those pages back up.
If you do redirect, all your inbound links, users' bookmarks, and most of your current rankings will be preserved.
So why don't search engines have a "reset" button? Because there are almost always better options. In your case it is much better to redirect.
In the case when a site is penalized, Google doesn't provide a reset button because that might remove all penalties.
So how do you implement the redirects? You need a list of your old URLs. You may have a sitemap from your old site that you can start with. You can also get the list from your server logs, Google Analytics, or even from Google Search console.
If you planned ahead, your URLs in your new CMS will be similar and you can implement a rewrite rule to handle them. If there is a pattern between the old and new URLs, it can be a one liner in a .htaccess file to issue the redirects for the entire site.
If you have to manually find the new URLs and map thousands of them one by one, you could look into