"This is my first time taking part in a soccer match."
I did this, too, and was marked wrong
When I tested this with google translate I got:
这是我第一次参加足球比赛 This is my first time participating in a football/soccer match.
这是第一次我参加足球比赛 This is the first time I participated [sic] in a soccer/football match.
ie ...it seems to take the 'my' away in our preferred sentence. Whether or not this is relevant, and both should still be accepted, I have no idea.
Hope that helps
I don't have a grammatically sound explanation on this and is purely speaking as a person who uses the language (Mandarin in mainland China) as a near-native speaker, so please take what I say with a grain of salt:
With 的: There is something really awkward and unnatural about having a verb following a possessive adjective. similarly you wouldn't really hear phrases like 我的吃饭 or 我的跑步。
Without 的: The 我here is no longer part of a possessive , but the subject of the verb, and the sentence sounds more natural.
No, neither unusual nor ungrammatical. You can use an adj phrase with the present participle'"..participating..." It modifies 'time' similar to the way a relative clause would. https://www.phrasemix.com/phrases/someones-first-time-doing-something