Submit Website URL in Google webmaster tools helps to index your site fastly.

For fast indexing, fetch your website on Google webmaster tools.

in order to index your post quickly follow these Things
-Ping your website using pingler,ping-o-matic and pingoat
-Fetch that url using Google webmaster tools
-Fetch that ur using Bing Webmaster tools
-If you are using wordpress,Update your ping list

If you want that your site index fast in Google than you go in webmaster & select the fetch as Google option after that you do some submission on high pagerank sites like social bookmarking,article submission & share you site links facebook groups and communities.

-Ping your website,
-Post new and unique content,
-build internel links,
-build deep links,
-submit to social bookmarking site,
-comment on high quality blog,
-forum posting,
-image and video submission,

Go to Google Search Console.
Navigate to the URL inspection tool.
Paste the URL you'd like Google to index into the search bar.
Wait for Google to check the URL.
Click the “Request indexing” button.

Google Search Console is the best and strong platform where you can fast index your website.

- Update Sitemap
- Using Google Search Console ads web page links
- Blogs / Article using quality content
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Yes, the above are also good points where our website will get indexed.