Point 404 pages to homepage

EDIT 2:
You could also make a function to load your front-page.php template for 404 pages. See below:

add_filter('template_include', function($template) {
    if ( is_404() ) {
        return locate_template(['front-page.php']);
    }
    return $template;
});

EDIT:
I read over the fact that you want to keep the URL as is. Why is that if I may ask?

You could make a redirect from your 404 page to your homepage. Just edit (or create if it doesn’t already exists) your 404.php file within your theme or child-theme folder. Below snippet redirects all 404’s to your homepage:

<?php

header("HTTP/1.1 301 Moved Permanently");

header("Location: " . get_bloginfo('url') );

exit();

?>

I usually don’t recommend this, but I’m going to assume you have a good reason for it.