Installing to subdomain while there's existing installation in main domain

I have a wordpress at my website called example.com. I want to install a separate wordpress at a subdomain: subdomain.example.com. I don’t think I want a multi-site installation because these sites are very unrelated in content and will be unrelated in look and feel and in features.

Is there a walk-through for doing this?

Here’s where I got on my own:
– The subdomain document root is public_html/subdomain. There is currently no redirection (does there need to be?).
– I installed wordpress (via my hosting company’s automated install accessable from the cPanel, which worked just fine for my first wordpress installation) into public_html/subdomain.
– The hosting company said the link for me to access the wordpress site would be: example.com/subdomain/wp-admin, but when I clicked on this I got my standard website’s “content not found” page.

So, my questions (other than hoping there is some kind of walk-through for this) are: (1) Where do I install wordpress, (2) What kind of redirecting for the subdomain do I need to do, and (3) How do I log into my wordpress installation?

Do I need to do something with wildcard DNS? It looks like this is for networked multisite, but maybe this is also for my scenario?

Sorry if this is a duplicate, I have tried searching for hours but honestly haven’t found much to help, everything I come up with is forum posts that are three or four years old and don’t really address my issue.