Agree wholeheartedly. I've gotten this wrong twice now and will, evidently, forever, because "we almost arrived" is nonsensical.
It would work as "we've almost arrived," present perfect, but not simple past tense "we almost arrived," unless you're telling a story about what happened in the past--a different concept than this exercise
Can you not say " Yes, we almost came" which might be followed by "but we changed our minds" for example or would this be said in a different way?
I would say, "Мы думали приехать, но передумали." Or, "Мы чуть не поехали," "We almost went [to the party or whatever]."
"Мы почти приехали," translates as, "We're almost there."
"We almost came," implies that a decision was made not to come [to the party or whatever]. That's a different thought than, "We're almost there," which is essentially what this exercise is saying.
Would a sexual meaning, like "Yes, we almost came" be expressed the same way?
No. For sexual meaning, you'd probably use «ко́нчили» 'finished'.
In the modern lanugage the word «ко́нчить» is usually avoided in the meaning 'to finish'; instead, we use «зако́нчить» or «око́нчить» to avoid sexual associations. Older sentences with this word often sound funny.
For example, Lermontov's Mtsyri, part 24, has lines «Я ко́нчил. Верь мои́м слова́м // И́ли не ве́рь, мне всё равно́.» 'I've finished [my story]. Trust my words, // Or don't trust, I don't care.' This sounds like "I came." now.
(This poem is pretty well-known here, you can listen to it on youtube. This exact phrase is on 50:26. English translation is "I will say // No more, you know the rest. [...] // [...] // Believe me not, 'tis all the same"; another translation is "I've finished, for you know what more // there is to tell. Believe me or // Believe me not — I do not care").
For the same sentence in English we will often say "almost made it". I honestly cannot think of an example of saying "almost arrived". For examples: "They had dinner at six." Response: "I almost made it." Or "The flight left at 7." Response: "I almost made it." If you used "arrived" here instead, it would sound odd. To contrast with a few more examples: "I almost did not arrive."/"I almost did not make it." "I almost made it to her house."/"I almost arrived at her house." Arrived, to my ears, sounds odd here.
Would "Yes, we're almost there" be an acceptable translation? It sounds much more natural to me (American English).