Christians believe that the only way to God is through Jesus, and no other religion will lead to God. This is not because of arrogance or intolerance of other religions. To be precise, we are talking about the God of Abraham, Isaac, and Jacob, the God who created the universe, the heaven and earth, and the giver of life. I will not deny that some other religion might lead someone to some other deity who is not this particular one. For example, if someone rather prefers to worship the Flying Spaghetti Monster as their god, it is really their personal choice, but we are not concerned with men-made gods who has no breath and cannot give life.
But what is the basis of our claim that the only way to the life-giving God is through Jesus? It all started from the promise that God made with Abram the great father, that God will give Abram a son through which Abram will become Abraham, the "father of many nations." Through this son, God will bestow upon Abraham as countlessly many offsprings as there are stars in the sky. God made a unilateral covenant such that if God did not fulfill the promise, God would suffer the consequence of death: cut and arranged in halves as Abraham did to the sacrificial animals of the covenant making ceremony. This is the account written in Genesis 15.
But how do we know that God is truthful to His Word and faithful to His promise? This is why God asked Abraham to offer his son Isaac as burnt sacrifice to God, as written in Genesis 22. Casual observers might decry that this is a selfish God demanding to be glorified through the savage act of child sacrifice. These casual observers might use this as evidence that God is unfaithful to His promises. It might first appear that both Abraham and Isaac were being naive and just blindly following the instructions. We as readers tend to think we are wiser than the characters in the story, but there is a twist. When Abraham said to Isaac, "God himself will provide the lamb for the burnt offering, my son," did Abraham lie in order to dupe his son into becoming child sacrifice? And would Isaac, in teenage or early twenties at that time, be stupid enough to allow his dad to tie him up in a rope after Abraham built the altar, with the object of sacrifice still missing?
I think neither Abraham nor Isaac were as naive as it first appears. They knew full well about God's unilateral covenant in Genesis 15, in which God would bear the consequence of death if the covenant is broken. And in Genesis 17, God said He will establish the covenant with Isaac. So if Abraham killed Isaac in Genesis 22 as God appointed him to do, there would be no one else to fulfill the promise. Abraham would cause the death of God if God were truthful, or find out that the god he served is untruthful and unworthy to be served. In the end, God stopped Abraham when Isaac was about to be killed, and God provided a ram as the sacrifice offering.
So this test is really a reading comprehension test to see if Abraham understood God's promise and God's character. Abraham followed God's direction, but he knew God would not contradict Himself. That's the faith of Abraham, and that's how we know the God of Abraham, Isaac, and Jacob is a faithful God who will fulfill His promise. I also think that it is remarkable that Abraham did not purposefully kill Isaac in bad faith, so Abraham indeed deserves to be the great father of many nations.
As for the rest of us, we are unlikely to individually make a covenant with God, but we have the option to accept the covenant of Abraham through Jesus Christ which we may participate as our inheritance. Abraham is the reason why there is no other way to God, and there is no religion that will lead to God, except through Jesus, whose surrogate parents are both descendants of Abraham even though Jesus is really God Himself. Jesus is God incarnated to become the Son, who took the place of Isaac to be sacrificed as the ultimate offering.
And no other gods can do that for us.