Custom Landing Page

I am currently using a theme on my wordpress site. However, I am wanting to create a parallax custom landing page for the website instead of using the theme which would take the place of my home page but then when enter I could still get to my home page as https://www.whatsahead.com/home. I am struggling to figure out the best way to do this. I would be creating the landing page in Muse and can export the HTML, CSS, scripts, and links from Muse. Part of the problem is my current theme does not use templates. I would build a custom template for that page but the current theme I am using does not have templates. In fact it is built with an index.php that points directly to a php page that uses modules to build the unique pages. (no page.php either). I know enough php to edit a file, but not often build anything from scratch or how to make the theme have templates when none exist. I know I could just move the whole site to whatsahead.com/home with the home page pointed to this sub-site, but would it mess up the rest of my links (like would whatsahead.com/about now have to be whatsahead.com/home/about? Anyone have any thoughts?

Thanks!
Lindsay