I want domain.com/stats to be present by default

If you want webalizer or awstats pages to be available by default for new domains, you can do so by creating:

/usr/local/directadmin/scripts/custom/domain_create_post.sh

In the file add the code

#!/bin/sh
ln -s ../stats /home/$username/domains/$domain/public_html/stats
exit 0;

Then chmod the domain_create_post.sh script to 755.

If you want it to be for awstats, then change the bold stats name to be awstats instead.