To answer this question one must answer what does Ἑβραῖος ἐξ Ἑβραίων mean? Here are examples of how translations have translated it:
a Hebrew of Hebrews (NAS, ESV, NIV, ASV, NET, ISV, Darby, YLT)
a(n) Hebrew of the Hebrews (KJV, NKJV, D-R)
a Hebrew born of Hebrews (HCSB, NRSV)
a Hebrew born from Hebrews (LEB)
a Hebrew of Hebrew parentage (NAB)
I am a Hebrew, and my parents were Hebrews (NCB)
hebreo de hebreos (RVA, LBLA)
עִבְרִי מִן הָעִבְרִים (HNT-Bible Society of Israel)
an Ebrue borne of the Ebrues (Tyndale 1536)
a Hebrew-speaker, with Hebrew-speaking parents (CJB )
a real Hebrew if there ever was one! (NLT)
I am a true Hebrew (CEV)
I’m a pure-blooded Hebrew (GW)
a Hebrew [and the son] of Hebrews (AMP)
a pure-blooded Hebrew (GNB)
If the ἐξ preposition weren’t present this would be the meaning. It’s interesting how many translations translate “Hebrew of Hebrews” that seems to imply this interpretation.
While Paul wrote in Greek, Hebrew of Hebrews is a Hebrew way of expressing the superlative (note Holy of Holies):
(i) The absolute superlative, which manifests the outstanding feature, condition or state of something or someone can be expressed by:
a. A singular noun in the status constructus preceding the indefinite plural form of the same word.
vanity of vanities = utmost vanities (Eccl. 1:2)
Van der Merwe, C., Naudé, J., Kroeze, J., Van der Merwe, C., Naudé, J., & Kroeze, J. (1999). A Biblical Hebrew Reference Grammar (electronic ed., p. 236). Sheffield: Sheffield Academic Press.
If the superlative were the case, Jewish Christians would understand it to mean Paul was the most Hebrew that one could be, and he defends this in the verses that follow.
However, the question is what does ἐξ mean? The simplest meaning is
89.142 ἐκ; ἀπό: markers of the substance of which something consists or out of which it is made—‘of, consisting of, out of, made of.’
Louw, J. P., & Nida, E. A. (1996). Greek-English lexicon of the New Testament: based on semantic domains (electronic ed. of the 2nd edition., Vol. 1, p. 795). New York: United Bible Societies.
However, the translation “Hebrew of Hebrews” is very unclear as shown previously, especially to a Hebrew. Note the Hebrew translation translates ἐκ/ ἐξ as מִן (from) and the Complete Jewish Bible translates it, “a Hebrew-speaker, with Hebrew-speaking parents.”
This is also how Robertson explains the phrase:
A Hebrew of the Hebrews (Ἐβραιος ἐξ Ἐβραιων [Ebraios ex Ebraiōn]). Of Hebrew parents who retained the characteristic qualities in language and custom as distinct from the Hellenistic Jews (Acts 6:1)
Robertson, A. T. (1933). Word Pictures in the New Testament (Php 3:5). Nashville, TN: Broadman Press.
Note that when the translations express the meaning using more than “Hebrew of Hebrews,” they express it as meaning a Hebrew from Hebrew parents.