Was at least part of the Savior’s suffering related to his death on the cross?

Hi Gramps.
I have a question about the Savior’s atonement. I am confused about some parts of it. Jesus died for our sins. He died on the cross. But many people died on the cross. It was the Roman’s cruel common punishment. I know that the Savior atoned for our sins in the Garden of Gethsemane. That is where the pain was so great, he sweat blood. After that he was crucified. Yet I hear often that Jesus died on the cross for our sins. I always thought he suffered for ours sins in the Garden and then died on the cross because of being set up by the corrupt leaders after he declared his divinity. Did Jesus in fact die on the cross for our sins? Or did he seal his testimony with his blood and that happened to be the method but the atonement happened before the crucifixion.
Kathleen

Dear Kathleen,
The Savior died on the cross for us, but the atonement, i.e., the payment to the law of eternal justice for all the sins of all mankind on all the infinite worlds that He created was fully paid before his death. While yet on the cross He said, it is finished—
When Jesus therefore had received the vinegar, he said, It is finished: and he bowed his head, and gave up the ghost John 19:30.
Gramps