Quick Question for My Non-Reformed Brothers & Sisters in the Lord

I have a question that I have had running through my mind today and so I thought I'd ask to see if I could get a good answer.

Is unbelief a sin?  In other words is refusing to believe the Gospel and accept salvation through Jesus Christ a sin?

Seems like the only answer to the question is "yes" and I would agree. However I think this creates a problem for most believers that I know.

Most believers that I know would say that Jesus died for every sin that has ever been, is being, or will be committed. If that is so then it seems to me that the only logical outcome is for everyone to go to Heaven, i.e. universalism, because Jesus has paid the price for every sin that everyone ever committed.

I have challenged a few people with that line of reasoning before and every single one responds with the same answer, "Yes, Jesus died for their sins, but they refused to believe and accept His offer of salvation." I have never asked the following question because I never thought of it until now.

Is refusing to believe and accept Jesus' offer of salvation a sin?  If the answer is yes then Jesus died for that sin and God has no grounds for punishing you for it since He already punished Jesus for it.

You might respond, "Yes, there is punishment for it because Jesus' payment for it was never accepted." To which I will respond, "Was that a sin for a person to never accept that payment?" If the answer is yes then Jesus paid the price for anyone's refusal to accept the payment of their sin. And now we start over.

If Jesus died for all sin at all times and unbelief and refusing to accept salvation through Christ is a sin I do not see how universalism is not true.

Looking forward to hearing the responses.