Link to “Index.php” when “Home.php” is present

I know this exact same question has been asked no less than twice before.

I searched the old threads and could not find a proper response. Most of them were for another issue/goal in mind or simply told people to use Static home pages.

Is there a way to link to or a workaround to have a “splash” type page like the static home page but still remain dynamic? Right now what I have is a “newspaper” like home.php that calls the first couple posts of multiple categories along with their graphics to make a really neat landing as if it were a newspaper literally.

While that is fine and dandy and my section (category) links display the index.php template it will only list the posts in that category. Besides making every category a a child of “Main” or something and linking to that category is there a way I can link to a global archive, date sorted, as the index.php would display if home.php was not present?