You should create an XML sitemap and dynamically add new dynamic URLs to it. There is no need to use lastmod in an XML sitemap. Google says they ignore lastmod because few sites keep it up to date. Googlebot will notice any new URLs in the XML sitemap and will come crawl them whether on to they have a lastmod specified.
You should not create a single ...
In some cases, the image URL may not be on the same domain as your
main site. This is fine, as long as both domains are verified in
Search Console. If, for example, you use a content delivery network
such as Google Sites to host your images, make sure that the hosting
site is verified in Search Console. In addition, make sure that your
robots.txt file doesn’...