Submitting your sitemap is the first step, which allows Google to find your URLs easier, but it won't request indexing by itself.

You have the option to go to the Google Search Console and request indexing manually for pages that are listed as "Discovered - Not indexed" or similar, but this is limited to 10 requests per day.

This tool uses Google's Indexing API to perform URL indexing requests on your behalf on auto-pilot for pages that are not yet indexed.