You can set a unique page up for the splash screen, and make it the home page in the config.
return [
'home' => 'splash'
];
Then your existing home page should be accessible at /home
. No need to ajax it i dont think, unless you still want it to load over the home page to reveal it. There are a few javascript page transition libraries out there that will make it feel like it is loading over the page, despite being separate pages.