It's perfectly correct to use the continuous -ing form to talk about the past. It doesn't matter that this action is finished. This is an example of the Past Continuous. It describes an action that took place during a specific time period. And it's often used to develop the background to a story. You can also use it an unreal, hypothetical situation like this... there's probably another clause that is omitted/implied (something like "If we had known that the train would be late.").

Sorry but this is not past continuous. It's a gerund and it work in a similar way as an infinitive.

We could have taken ouR time to go to the station. No -ing needed. You would use -ing if it's still going on. We're getting to (= on our way to) the station, but we can take our time, as we are not in a hurry, and the train is not there yet. BB - Basler Biker

*It is*

*works