No, Jews don't have their own pathway to God.

"I told you that you would die in your sins; if you do not believe that I am He, you will indeed die in your sins." -Jesus (John 8:24)

And, as if that wasn't clear enough: "Whoever believes in the Son has eternal life, but whoever rejects the Son will not see life, for God's wrath remains on him." -John the Baptist (3:36)

Or for those false teachers who revoke the gospel of John as some mythical piece of apocrypha, from Luke:

"I tell you, whoever acknowledges me before men, the Son of Man will also acknowledge him before the angels of God. But he who disowns me before men will be disowned before the angels of God." (12:8-0)

"...he who rejects me rejects him who sent me." (10:16)

And from Mark: "If anyone is ashamed of me and my words in this adulterous and sinful generation, the son of Man will be ashamed of him when he comes in his Father's glory with the holy angels." (8:38)

So Paul can say: "What Israel sought so earnestly it DID NOT OBTAIN, but the elect did."

Jews do not have their own pathway to God because they refuse to acknowledge that Jesus is the Christ, the Son of the living God. They deny that he died on the cross for the sins of the world, and that he rose from the dead. They deny that He is Lord of all. They do not confess Him and do not believe in Him. And, inasumuch as the law, the prophets, and the psalms testify primarily to the gospel of Jesus Christ, they have rejected the oracles that were entursted to them.

And so we may repeat to modern jews the very question that was put to them in the first century: "If you believed Moses, you would believe Jesus, for Moses wrote about him. But since you do not believe what Moses wrote, how will you acknowledge what Jesus says"?