SERP Propagation
There seems to be no fixed time for a search result to become available across all servers. Getting Google to crawl your page and to index it is pretty easy to do by making a request in Google Search Console.
My experiments have shown that this can happen within 24 hours but it could take much longer. When you submit a request for a page to be indexed in GSC it is also easy to check that it has been indexed by making another URL inspection.
A further observation is that a page submitted in sitemap but not specifically requested to the indexed was reported as being included in the Google index but did not appear in a SERP when a non-ambiguous query was made. In this case there seemed to be a positive correlation between the request for indexing and the inclusion in a SERP. I cannot be sure that this is the case.
Re-Indexing pages
If you are making changes to a webpage and you want these changes to be found by Internet users making a search then you need to make a request for the page to be re-indexed. If you don't do this then your changes will take considerably longer for searchers to find.
You have to make sure that you don't exceed your quota of pages that you can get re-indexed on demand
The use of Google Search Console
Making a request to have edited pages re-indexed using GSC is key here. Using the URL Inspection tool will allow you to determine waht actions you should take with your pages.