How to add www to WP site?

I have set up dozens of wp sites like this and never had a problem.

It is 1st time I am facing a problem with this.

This might have to do with the aliasing of the domain on your hosting account or server Puneet; you can check to make sure that www. and non-www are "pointing" to the correct content folder (something like a www-root)

Structure-wise, some servers have (relative to some arbitrary "user" folder, maybe):
domain.com (point to some domain-root folder, we'll call /user/domain.com for now)
www.domain.com would then "point" to /user/domain.com/www

In which case, re-aliasing the domain or sub-domain to the correct content folder would help, alternatively enforcing a URL-based redirect through an .htaccess file (or an HTML or php-based redirect file, which are easy to correct but not 100% effective in all cases, depending on how the directory is accessed).

If this doesn't work, there may be some URL's that are incorrect in the WordPress database itself (this requires phpMyAdmin access to check the DB directly; there are plenty of online guides for using phpMyAdmin to check the WP URL directly in the DB itself.)

Hopefully one of the above helps.

By adding that setting into WordPress, it automatically creates a redirect for you.

Correct, no redirect is needed as WP will take care of that for you. This actually stores it in the database.

An .htaccess-based redirect will redirect all files referenced from the affected directories.
Redirect via htaccess without updating the URL can effectively impose a redirect "loop", in a sense (so be careful in using it).

as an example: htaccess rules enforce www.*, wordpress URL enforces non-WWW, which can possibly cause problems. Some host servers can compensate and correctly stop the loop, and some will refuse to serve any info at all.

(I stick with the Wordpress URL at www (personal choice) and let the permalinks/canonicalization be handled by the WP admin, and avoid fiddling with .htaccess too much).