Change index.php to something else

My client is currently on wordpress and they wanted me to put a static website up there as an in-between till we migrate over to wordpress with the new rebrand.

We still use a lot of the old content and links, but only want people to go there if we are linking to it or if a link is existing in print materials.

I’m wondering if there is a way to keep both a wordpress install and a static website up at the same time.

WordPress uses the index.php, is there a way to tell wordpress to use something like default.php or website.php or oldwebsite.php as the “index.php” that contains all of the loops and fall back?

I’m sure there has to be a way where you can include it some config file or settings, but I haven’t ran into it yet.