This is a good question, and to my knowledge it's never answered on-screen.
But what's interesting is that in order to prevent a paradox there must be an answer. The clock needs to be broken (or, at least, everyone needs to think it is broken).
If the clock works, then there's no need to fix it, which means no fliers being passed out by the Hill Valley Historical Preservation Society. No fliers means Marty doesn't have one to show Doc in 1955. But even more fundamentally, if the people of the city don't believe the clock was struck by lightning at 10:04 PM on November 5th 1955, then Doc and Marty have no way of anticipating that lightning will strike then. That means Marty can't get home. Marty not going home means lighting will strike the clock and break it, which allows for the flier and all that, which means they will know when the lightning strikes, which means they use it, which means the clock doesn't break....paradox.