grammar - Question about articles: Why is "before the train came" correct?

Example sentence:

I had a little time before the train came.

Would you please explain to me why it is correct to use "the" before "train"? My teacher told me that "the" is used before objects well-known to both speakers and that if a noun is used for the first time we shoud use "a".

But in this example the speaker uses "train" for the first time. Moreover we don't know about this train, so we must use "a train", not "the train". But it was a native speaker who said it; what exactly did he mean to say?