I keep getting tricked by this, but I try to remember that subjects don't have a preposition in front of them (eg, 'il momento', not 'allo momento'). This helps me realize that it's the moment (or time) that's coming, not something coming to the moment.
You can say (both correct): "che era venuto il momento" or "che il momento era venuto". No preferences.
Yes, I wrote the same: "I heard that the moment had come." I heard, because someone told me. Why is it not good?
Because "I heard" would be translated as "Ho sentito". "Sentivo" could mean "I was hearing" but since there is no context (... was hearing when?), you can't translate it that way. Whereas "I felt/I was feeling" tells the same thing. Clearer now?
In initial Italian sentence there is "Sentivo" which is Imperfetto and not Passato prossimo (ho sentito)
I put "I felt that the time had come." which is more common in English than "the moment had come". Lost heart.