Thanks so much — I already had the 'destroy on layout' behavior set, but I was a dummy and the sprite was inside the layout on the start of the game. I moved it outside of the layout and it stopped happening. Thanks for taking time to answer my dumb question and help.
Also, your idea of using a separate layout for sprites is right on. I'm in the process learning Construct, and in that, I am learning how to keep things better organized and your suggestion is perfect for that.