Past perfect can be quite complex and should be used only when you are sure about the likely understanding. Even then, many people prefer using past simple with time hints. Quoting from Canonical Post #2
☛ ”Don’t use the perfect unless you need it.”
☛ Use perfect constructions to introduce prior eventualities as context for the current discussion.
In the case described in the question, there is more than one way of "telling the story", with different emphasis:
It started raining while we were on our way to the station. (Emphasizing the time the rain started at)
While we were on our way to the station, it started raining. (Emphasizing the fact that we were on our way)
We had not reached the station when it started raining. (Suggesting that you expected a different situation, in which you would have already reached it)
All the "stories" above take place in the past, and the time of reference is when the rain started, as seen by using the past simple tense "it started raining".
In contrast, the suggested sentence in the question uses past perfect "it had already begun to rain". This leaves the sentence without a clear time reference: since the rain is now is prior event, to what point in time does "already" refer to? Without a time reference, the sentence sounds odd (this is maybe "the logic of English people").
A possible way to use past perfect in the second clause is to set the time reference to the point when you reached the station. If the story takes place at that time, then the rain becomes a prior eventuality.
- When we reached the station, it had already begun to rain.