Sitemap: Should I dynamically update sitemap for dynamic content or create a page containing all the dynamic links

Say i have the following route http://<my-domain>/{category}/subjects/{id}/Sitemap: Should I dynamically update sitemap for dynamic content or create a page containing all the dynamic links

the ones in the brackets are dynamic, I’m struggling with what is better or any better way to let google crawl through all these dynamic links

Approach 1: manually doing the job by removing or adding the record to site map and updating <lastmod>

Approach 2: create a page that includes all those links and reference that page in sitemap.xml

The second approach can be generated as a plain html file which is generated from the server app. Or, a simple webform aspx page that dynamically generates those links without having to create an html file.