Jesus Christ was sent from heaven when He incarnated as a man. Isaiah 9:6, For a child will be born to us, a son will be given to us; And the government will rest on His shoulders, And His name will be called Wonderful Counselor, Mighty God."
Then there is John 6:42, John 3:13, "No one has ascended into heaven, but He who descended from heaven." One more verse out of maybe 10 or 11 more. John 6:36, "For I have come down from heaven, not to do My own will, but the will of Him who sent Me."
Now, common sense and logic dictates that if one is sent they had to have preexisted. John 1:1-3 and many other verses prove Jesus preexisted His incarnation as a man. As the "Logos/Word" He was with God and was God.
John 1:3, "All things came into being by Him, and apart from Him nothing has come into being that has come into being." Please explain to all of us here how without Him "all" things have come into being. Colossians 1:16-17 supports this and eve His own Father supports this at Hebrews 1:10.
Moreover, Revelation 3:14 explains that Jesus Christ is the "arche." the beginning of creation. We get are English word "architect" from the Greek word "arche." An architect is a person who plans, designs, oversees and is the "origin" of anything that is built or created.
Also, I find it interesting you happen to have brought up John 10:36. Did you read the context? At John 10:30 Jesus says, "I and the Father are one." "One," (hen) is a neuter number to indicate equality of essence, attributes, design, will, and work. It is already obvious that the Father and the Son are one in purpose according to the context of John 10:25-29.
How? Because the sheep are equally safe in the Fathers hands as well as in the Son's hands. Also at John 10:28 Jesus gives them eternal life and they shall never perish. How is it that a man, who is not God can give other men eternal life?
Getting back to John 10:30 and what Jesus said why did the Jews pick up stones "again" to kill Him? Do you really think it was for being one in purpose? The Jews at John 10:33, "For a good work we do not stone You, but for blasphemy; and because You being a man, make Yourself out God." Can you give me an example of someone accused of blasphemy for being one in purpose?
And what's most interesting is Jesus bringing up Psalm 82:6. "Has it not been written in your Law, "I said, you are Gods?" Jesus Himself brings up the subject of "gods" for a reason or to make a point?
Which brings us to the verse you quoted, John 10:36. Jesus' usage of Psalm 82:6 was to imply that what the Scriptures call humans "allegorically, He was in actuality since He does what only God can do. Forgives sins, raise the dead, gives eternal life etc.
Since at vs35 the Scriptures cannot be annulled, how can you say that the one whom the Father has sanctified and SENT INO THE WORLD is blaspheming because I said, "I am the Son of God"? Vs38, "If you don't believe Me, believe the works, that you may know and understand that the Father is in Me, and I in the Father."