Hi palwindersingh and welcome to WebmasterWorld [webmasterworld.com]

You don't mention what you have done to offer Google information about your site so I'll try a few basic ideas to start with. To see what Google understands about your site, you can create a Google Search Console account where you can see what comments and activity they have regarding your site.

In your GSC interface you can see their interaction with your sitemap once you have submitted it. You can see issues that might need more work, like meeting Core Web Vitals.

You can also view your site's logs to see how often they crawl and what pages they visit.

What are the activities I can perform to get a page indexed?

Ensure your pages are up to standards for viewing on mobile and desktop devices and be sure your pages load fast and offer navigation that is user friendly, accurate meta data. Check for errors in html, js and css that might cause problems.

Visit Google's "how to" site to ensure you are doing things in your best interest: https://web.dev/

In my opinion, Google has been having problems with indexing pages for some time now. It's worth remembering about Bing and putting your sitemaps there too. Smameu I use Google less and less because its search results are irrelevant - currently completely bad.

Maybe it's time to pay more attention to Bing and other search engines. There are more and more such signals from what I consider to be completely harmful Google.

Standard questions:
#1 How do you know pages are not getting indexed? Have you done exact-text searches, or is G### telling you so? (Do not take GSC’s unsupported word for anything!)
#2 Are the pages being crawled regularly? Without an answer to this question, no other questions can be addressed.

Normally, how much time it takes for Google to index a web page?

I’d say less than 24 hours--a few days, tops--unless you have a multi-thousand-page site that has been unrolled all at once.

It's depends upon category if you pick up good niche and narrow down like
Domain is health and subdumain is children health. In this conditions you easily rank.
Others wise you should use such content already use your competitor.
And implement on your web page

Did you add a sitemap.xml file and submit that to Google?