Good question. The phrase "of God" appears 3 times.
John 8:47
English Standard Version
Whoever is of God hears the words of God. The reason why you do not hear them is that you are not of God.”
In the 2nd appearance, it is words of God, rhēmata Theou, genitive. The English preposition of is implicit in the genitive. It means words spoken by God.
In the 1st appearance, the Greek is ὁ ὢν Θεοῦ.
ὢν (ōn)
Verb - Present Participle Active - Nominative Masculine Singular
Strong's 1510: I am, exist. The first person singular present indicative; a prolonged form of a primary and defective verb; I exist.
I would translate this as
The one being God's
Is Jesus implying that whether someone is “of God” or not is inherent in who they are and not by choice (ie choosing to obey Jesus’s words)?
Yes, to some extent. The Greek does carry this sense of meaning in the phrase ὁ ὢν Θεοῦ.
In the 3rd appearance, the Greek is οὐκ ἐκ Θεοῦ.
ἐκ (ek)
Preposition
Strong's 1537: From out, out from among, from, suggesting from the interior outwards. A primary preposition denoting origin, from, out.
I would translate this as
not from God
Is Jesus implying that whether someone is “of God” or not is inherent in who they are and not by choice (ie choosing to obey Jesus’s words)?
Yes. Now the case for this argument is even stronger.
John 10:27 also support this line of thinking:
My sheep listen to my voice; I know them, and they follow me.