Any water intrusion from the passenger side of the front cap could end up where you found it. I'm thinking of others who had leaks from the top running lights that wound up in the stairwell. Water coming in can run down the frame to the bulkhead and onto the stair. Same with windshield.
An inch of water is a lot. I would expect you could find the entry point using a hose, but you may need an assistant to sit by the stairs as you try different areas.
Larry, Eileen, and Finley
2004 Alpine 36FDDS
Third motor home, first Alpine, no need for another.