Toy problem to motivate the idea of advanced Green's functions

In summary, the concept of advanced Green's functions is illustrated through a simple toy problem that highlights their utility in solving differential equations. This approach emphasizes the importance of understanding the solution structure and the role of boundary conditions, ultimately showcasing how advanced Green's functions can facilitate the analysis of more complex physical systems by providing a systematic method for incorporating initial and boundary value problems.
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Swamp Thing
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The Wikipedia article on Green's functions says,
the solution provided by the use of the advanced Green's function depends only on the future sources and is acausal. In these problems, it is often the case that the causal solution is the physically important one. The use of advanced and retarded Green's function is especially common for the analysis of solutions of the inhomogeneous electromagnetic wave equation.

What would be a really simple physical toy problem that would motivate and explain the concept of advanced Green's functions?
 
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