Translation:By passing through this door, we have arrived before the others.
Bizarrely, "on est arrivés" can be correct, according to the Académie française.
(Also, see http://www.academie-francaise.fr/pauvre, which gives some examples but is less explicit about the rule.)
Specifically, to agree with the subject "on", the past participle should be singular or plural depending on what you actually mean. When you use "on" to refer to certain specific individuals, you treat it as plural.
The article also suggests avoiding the use of "on" in sentences where you'd have to write this, because it looks weird.
If you mean on=we, then it must be treated as grammatically plural, even though the verb is conjugated in 3rd person singular. So any adjectives or relevant past participles must agree in number and gender with "on" (when it means "we"). https://www.thoughtco.com/the-many-meanings-of-the-french-subject-pronoun-on-3572148
The primary, main use of "on" is as the passive subject/agent - the English use of "one" in like manner derives from this practise.
Using "on" for "we" is a colloquialism (and incorrect, one might argue), although a widespread one.
The French penchant for using passive constructions with active meaning is a curious phenomenon. Should one understand it as the French trying to shirk away from being/feeling responsible for their actions and words, hmmh?! (I am kidding, but it is an interesting trend.)
I am confused why “On passing through that door, we arrived before the others.” was marked as incorrect. I thought the perfect tense could be translated as simple past in English, so the omission of “have” should be OK. And my dictionary gives “on arriving” as the translation for “en arrivant”, so why not “on passing” here?