"This is my first time taking part in a soccer match."
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.
Putting the subject with the verb (这是第一次我参加足球比赛) feels like a more natural word order to me. Should this be acceptable?