Installing wordpress into the same directory as existing static html website

I do not see any reason why it would not be possible. The main problem I see is updating the nav on the static pages as you move items into WordPress, but setting up redirects may make that easy.

There shouldn’t be any complex tasks to get this setup: install WordPress in the same directory as your static files, and that should be it. Confirm that index.php is loaded rather than index.html, and if so, then you’re set.