That's absurd!
If someone is condemned, that which causes condemnation is a sin, otherwise, they couldn't/wouldn't be condemned. Therefore, based upon your own statement, not believing is a sin because by it they are condemned. In effect, by not believing, they call God a liar.
For His elect on the other hand, His death included being forgiven for their sin of unbelief, the forgiveness of which, is why/how they come to belief. To not believe in Christ as the Saviour is not only a sin but it is the sin.
[Heb 7:25 KJV]
25 Wherefore he is able also to save them to the uttermost that come unto God by him, seeing he ever liveth to make intercession for them.
[Jhn 12:47-48 KJV]
47 And if any man hear my words, and believe not, I judge him not: for I came not to judge the world, but to save the world.
48 He that rejecteth me, and receiveth not my words, hath one that judgeth him: the word that I have spoken, the same shall judge him in the last day.