Submitting a new page to Google
If you are adding pages to your website you probably want Google to index them as soon as possible. If you wait until Googlebot finds the page, even if you do have the page listed in your sitemap, then, depending on how popular your site is in the first place, you may have to wait a long time. Even then, just because you submit the page using Search Console it may take some time to be found.
As always, the page must have unique content, and something that an Internet user might be searching for. This page, for instance, is unlikley to be found by a search as it only contains terms and concepts that are availble elsewhere on far more popular/important websites.
Add to the sitemap first
While this sounds obvious I have observered that if I submit a new page for indexing at the same time as the updated sitemap it is both unlikely to be crawled by Googlebot but it won't be indexed. Submitting the sitemap with the new page can be see being aceessed in your server logs and Google Search Console will tell you when you sitemap was last accessed. There is no point in requesting indexing unless the sitemap has been read.
Requesting page indexing
Search Console allows you to request a page be idexed but it seems to need the www subdomain: