If you cannot find an obvious simple example to introduce OOP, I wouldn't consider this as a problem, but rather as an indicator that OOP might just be a bit less elementary than you wish it were.
I have always found that 'pure' programming philosophies, like 'pure functional', 'pure declarative', 'pure OO' anyway do not hold what they (superfluously) promise. Look into some textbook on LISP or PROLOG programming and you will find imperative sequential methods have to be applied in time to make things work.
OOP, to be sure, is very convincing if you eventually see it working. I'll never forget how at the end of my first C++ lesson I thought: So this feels like real programming at last.
I believe there are experiences which you just cannot have right at the beginning. So why not accept that there is a HelloWorld Level first?