How is it to be justified as a belief that in order for God to hear our prayers we need to pray through Jesus Christ, in which certain belief systems claim that Jesus Christ is God to whom we are to pray to?
There are five versions of Jesus in the NT ─ those of Paul and the respective authors of Mark, Matthew, Luke and John. Of these five, those of Paul and the author of John are gnostic in outlook. The other three are not.
And unlike the other three, the Jesuses of Paul and of John pre-existed in heaven with God and (1 Corinthians 8:6, John 1:3) created the material universe, in the role of the gnostic demiurge ("craftsman"). The reason it happened that way is because the gnostic god is so exquisitely pure spirit that it would never occur to [him] to have anything to do with a material world, and [he] exists at a great distance from it. For those reasons, in gnosticism an intermediary between God and man is required.
While the idea of Jesus as mediator or advocate for humans has versions in the synoptics as well, the pre-existing and the creating of the universe are unique to Paul and John, and I can't think of an equivalent of John 17 in Paul or other gospels.
Another way of asking the same question is, ‘How is Jesus Christ the same GOD that we are praying to when we pray through him?’
The answer to this won't be found in the gospels, where each of the five versions of Jesus expressly denies he's God.
Jesus doesn't become God until the invention of the Trinity doctrine in the fourth century CE. The doctrine is peculiar in that the churches themselves admit it's incoherent, though the expression they prefer is "a mystery in the strict sense". But a mystery in the strict sense "cannot be known by unaided human reason apart from revelation nor cogently demonstrated by reason once it has been revealed" ─ their words, not mine ─ and if you work through that idea you'll find that it's the same thing as "a nonsense".
The incoherence problem would go away if the churches were to admit that the Trinity doctrine creates three gods, but that would create another problem, namely how does the Trinity decide things? One vote each? Father knows best? How?
But while the standard version remains, another incoherence follows. If there is only one will between them then God is only one person, who can appear in any of three forms (which is of course denied). But if each of the three has [his] own will, then how are decisions made? If there are no differences, no disagreements, then there is indeed only one will. But if God doesn't like idea X and Jesus and the Ghost are all for it, who wins? What is God's view of the matter? More incoherence, as you can see.