This claimed prophecy of Jesus references T'hillim / Psalm 90:2, but it also references Michah / Micah 5:2 (5:1 in the T'nach). Micah (the prophet) is simply stating that the messiah will be a descendant of King David, which per Jewish law and the Christian bible's various birth stories about him, Jesus was not. . .
The psalm simply states that G-d is from everlasting -- this is not a prophecy about the messiah. It is not about the messiah at all.
This psalm is a prayer of Moses -- as it says in the very first line "A prayer of Moses, the man of G-d. O L-rd, You have been our dwelling place throughout all generations. Before the mountains were born, and You brought forth the earth and the inhabited world, and from everlasting to everlasting, You are G-d."
Yet again it seems the list maker assumed no one would bother to actually check the "proofs" claimed as prophecies about Jesus. Not only is this a prayer by Moses -- but it clearly says in verse two that the everlasting one is G-d Himself, not the messiah!
The claimed "prophecy" fulfillment given is John 1:1 which says "In the beginning was the Word, and the Word was with G-d, and the Word was G-d."
Well, this certainly has nothing to do with T'hillim / Psalm 90:2 which states that G-d is eternal.
Neither does it have anything to do with Michah / Micah 5:2 (5:1 in the T'nach). The Christian bible misuses the words of the prophet Michah / Micah who said that the messiah will be a descendant of King David. It was David who was of Beit Lĕḥĕm–Ĕfratah. "And David was the son of this Ephraitite man from the House ofLĕḥĕm (Beit Lĕḥĕm–Ĕfratah, aka Bethlehem) of Judah." Shmuel Alef / 1 Samuel 17:12.
Michah / Micah 5:1 (2 in Christian translations) says “But as for you, Beit Lĕḥĕm–Ĕfratah... (there were two Bethlehems - Beit Lĕḥĕm–Ĕfratah was in the land of the tribe of Judah and the other was in the Galilee) you are too small to be among the thousands of Judah (so small you aren't even counted)- (but) from you [the messiah] shall emerge for Me, to be a ruler over Israel; and his origin is from of old, from early times (days of old).” The prophet Micah was stating that the messiah will be a descendant of King David (which Jesus was not if one believes in the virgin birth since lineage only passes from the biological father -- and G-d is not a son of David!). There is a blog post on this topic (link).
So there is no prophecy that the messiah will be born in Bethlehem. Just how many people do you suppose were born in Bethlehem? People are still born there -- Bethlehem of Judah still exists. Again -- something as ordinary as a person being born somewhere -- something that "fits" tens of thousands if not more -- is not and cannot be a messianic prophecy.
What of John 1:1 and the word (notice they capitalize the letter "w"?) was there in the beginning -- and somehow Jesus = this word? The "word of G-d" (and Jesus as the word) is just a repackaging of a pagan Greek concept of the λόγος / lōgos, the "personified word." It is an impossible notion in Hebrew and incomprehensible to the Jewish mind because the Hebrew word דָּבָר davar (word) is the closest thing that Hebrew has to a neuter noun and actually means a "thing", i.e. an inanimate object.
John 1:1 then invents a concept not found in the T'nach (Jewish bible) and is totally outside of Jewish teaching which is clearly that G-d is One (cannot be compartmentalized), and is not a human. John 1:1 in no way fulfills a "prophecy" in T'hillim / Psalm 90:2 which is about G-d being eternal or Michah / Micah 5:2 (5:1 in the T'nach) which states that King David was from Bethlehem and the messiah will be a descendant of David's.