Totally untrue! We have to first put in the work of actually believing. We have to first humble ourselves in truly inviting him to be our Lord and Savior. Here is where your contradiction is revealed. We can undo our own work that is a prerequisite to salvation.
Here's what I'm saying.
John 1:11-13 KJV
11) He came unto his own, and his own received him not.
12) But as many as received him, to them gave he power to become the sons of God, even to them that believe on his name:
13) Which were born, not of blood, nor of the will of the flesh, nor of the will of man, but of God.
When we choose to receive Jesus, believing in His Name, then God does something, begetting us, a new creation. We don't birth ourselves, that is entirely from God, as He knows our heart towards Him, if we have believed Him.
After we are born from God, what is it that we would undo? Having received Him? Having believed in Him? Now we are born of Him. We're competely past that point in time, and we've become new creations, sharing God's Own nature, with His commitment to us to keep us safe unto an eternal salvation.
Only undoing our rebirth would change that, but God has given many assurances that this doesn't happen, that the end is sure for those who have believed and are reborn.
1 John 3:1-3 KJV
1) Behold, what manner of love the Father hath bestowed upon us, that we should be called the sons of God: therefore the world knoweth us not, because it knew him not.
2) Beloved, now are we the sons of God, and it doth not yet appear what we shall be: but we know that, when he shall appear, we shall be like him; for we shall see him as he is.
3) And every man that hath this hope in him purifieth himself, even as he is pure.
We know we will be like Him. We know this.
But here's the really important part for now, today. He who has "This hope" in him purifies himself. Knowing that we will in fact be like His is what causes us to purify ourselves now, in this life, today.
The surety of our salvation is what gives us the faith to overcome our flesh in this world.
Much love!