No, there was no other way; if there had been, God would have taken it, and would not have endured the agony of watching His only Son being put to death.
In fact, just hours before His arrest and death the Bible says Jesus fervently prayed that another way might be found to win our salvation, so He wouldn't have to endure the terror of what awaited Him. But there was no other way, and in a final act of perfect surrender Jesus accepted what He must endure on our behalf. The Bible says He "fell with his face to the ground and prayed, 'My Father, if it is possible, may this cup (of suffering) be taken from me. Yet not as I will, but as you will'" (Matthew 26:39).
Why was there no other way? The reason is because when we sin, we break God's law -- and because God is just, He can't simply ignore His laws or act as if our sins don't matter. If we break a law and are caught, we must pay the penalty for what we've done. In a far deeper way, when we break God's laws, the penalty must be paid -- the penalty of death and Hell.
But Jesus Christ paid the penalty for us! He was without sin -- but on the cross all our sins were placed on Him, and He took upon Himself the death and Hell that we deserve. Are you trusting Him alone for your salvation?