totally new, how do dynamic sitemaps help with indexing?

hi everyone, i'm super new to this whole SEO thing and just launched my first SaaS. it's called 'Dynamic XML Sitemap for Laravel & All Websites' and the main idea is to help with auto-updating sitemaps.

i've been trying to figure out the best way to get our new product pages indexed quickly by google and other search engines. right now, we're using a pretty basic, almost static sitemap solution, and it's just not cutting it. we're seeing some real issues with new content not getting picked up fast enough.

teh main pain point is that whenever we add new features or new content, i have to manually update the sitemap or wait for some cron job to run, which feels so slow and kinda tedious. i'm worried about missed opportunities for new content to rank, especially since we're adding stuff all the time.

i've heard a lot about dynamic sitemaps but i don't fully get how they work under the hood. like, how do they actually ensure faster indexing compared to static ones? is it just about always having teh latest URLs?

also, does using a dynamic sitemap improve things like crawl budget? my site is growing pretty fast, and i want to make sure google isn't wasting time on old or non-existent pages. i'm trying to optimize everything as much as possible, you know? any insights on how 'Dynamic XML Sitemap for Laravel & All Websites' specifically addresses these challenges, especially around making sure our crawl budget is used effectively?

help a brother out please, any advice for a noob would be amazing. really appreciate any guidance you guys can offer.