You’ve jumbled together many terms, making it difficult to follow what exactly you want to do ??
For reference, sub.example.com
is a subdomain, whereas example.com/sub
is a subdirectory. Also, there can be only one WordPress theme on a WordPress site, and you can’t install a WordPress theme without an existing WordPress site.
I’m going to assume:
1) You have an existing site at the root of your domain (example.com) that’s not built with WordPress.
2) You want to install a WordPress site in a subdomain (or subdirectory? You used both subdomain and subdirectory, so I’m not sure what you want).
This is possible, and, in fact, very common.
You may install the WordPress site manually, or use Softaculous — doesn’t matter, either one should work if done correctly.
If you want further details on this, please clarify what exactly you want to do: confirm if my assumptions above are correct, and clarify if you want to use a subdomain or subdirectory.
Standing by.