There is a nice expression that can be used in many contexts. It means "it's too late [for whatever]" similar to the English expression "You missed the boat": Поезд ушёл.
but "we are late" wouldn't also mean "мы опоздали"?
No, the "аЛИ" ending signals it is "were late".
The verb "to be late" would be conjugated if it was a present : "Мы опоздываем".
I'd disagree. Мы опаздываем is "We are about to be late", whereas "we are late" states the fact that it's too late - you've missed the train - hence, мы опоздали. "were late" is also опоздали, only not now - some time in the past.
If word "наш" is really necessary here?