Hi Kristen,
Is there a certain functionality you're looking to use with the splash screen? Like asking a user to agree to T&Cs?
From my knowledge, none of the storymaps currently have the capability of adding a splash screen OOTB - the closest might be in the Story Map Tour where you can use a point as an Introduction to the story map:
Like you mentioned, Web AppBuilder does allow you to include a splash screen, and so does the Basic Viewer so one of those could be embedded at the start of your storymap.
Otherwise it's worth adding this to the Ideas site: ArcGIS Ideas - these get implemented quite regularly.
Carmel