Translation:I have just been given a huge cake as a present.
Why could it not be подарил? If it's an unknown actor is it by default plural?
Yes. It is used when the specific actors are not important, so a generalized "they" is used.
Мне сказали, что я должен прийти.
Моё место заняли.
Мне назначили лечение.
У меня украли сумку. (Even if you know, that it was one guy)
Мне дали задание.
Меня назначили начальником.
Мне продали некачественный товар.
It is the most common way of translating the English Passive Voice into Russian
And also in English, "they gave me a cake" can be used as a (more idiomatic) substitute for "a cake was given to me" while "he/she gave me a cake" cannot.
Because «подарить» means "to gift", but I think your translation shouldn't be wrong.
Could 'I was only just given a huge cake' be accepted? Insisting on the translation of 'given as a present' is a bit harsh...
"As as a present" is indeed redundant. But I would use the Present Perfect tense: "I have just been given".
Is it correct to translate this phrase: "They just presented me a huge cake"?
No. It should be the translation suggested by DL, or "They have just presented me with a huge cake" or "They have just presented a huge cake to me".