Einstein grew up while the clock synchronization thing was
happening. I suspect it led to his interest in Time.
In 1884, the GMT was established. Einstein was born in 1879. He
would've been 4 years old, too young to remember it happening,
but it would've grown up with the IMPLEMENTATION and the
controversy of implementing a standardized set of worldwide
clocks.
I suspect it bugged him... this dissonance between the two views
of Time and it sparked his interest and curiosity.
I could be wrong of course. This is just speculation on my part
but I'm sure _somebody_ else made the same connection as me. I
usually find I'm not the first with ideas.