Is his required while using in spite?
Is it
In spite of his being young, he got the job.
or
In spite of being young, he got the job.
Is his required while using in spite?
Is it
In spite of his being young, he got the job.
or
In spite of being young, he got the job.
In spite of his being young, he got the job.
In spite of being young, he got the job.
Both the sentences are grammatical, without any difference in meaning.
Grammatically, you usually drop the possessive pronoun after the phrase "in spite of" when it's followed by "be" and the same subject is in the main clause. On the contrary, you cannot drop it, for example:
In spite of his being young, we gave him the job.
You can also rephrase the sentence presented by the OP as follows:
In spite of the fact that he was young, he got the job.
"In spite of" is like isolating something good or productive that may come out of a negative situation; with some contrasting or antagonistic factor that would hinder the latter.
It's a dependent prepositional phrase that mainly occurs at the beginning of a sentence.
e.g." In spite of the fact that the questions were tricky, Matthew scored high on the reading portion of the ACT."
The latter works, but I think the classic nominalization of to be young is young age, hence In spite of his young age.
Also, you probably mean despite or regardless, because in spite of means aversion.
Edit:
"his being young" seems almost wrong. "in spite of him" can be extended to "in spite of him being", where being is the participle forming a noun phrase. "his being young" is widely spoken though, I guess. (Edit: correction and another)