Custom static page/unique setup

Not sure if this has been covered in the forums here, but perhaps someone can direct me as I’m not quite sure how to search for what I’m looking for.

I have a client who wants a unique setup to their WordPress site. Essentially, they have a domain name and would like to use functionality similar to the static home page option within WordPress. However, they would like their ‘homepage’ to sit in a directory rather than the root of their site.

For example, if the site is located here: mydomain.com

And the blog is located here: mydomain.com/blog

They would like their homepage to be here: mydomain/homepage

However, the trick is that they would like all the other pages to have directories off the homepage as you would normally see in a standard static homepage. As such:

mydomain.com/about
mydomain.com/contact

Is there a way to make this happen without creating a separate HTML page?

Any help would be appreciated.

Thanks!