@Facade I don’t think the Bible is so clear on the issue. On one hand, the Bible suggests that the reason that someone would be rejected from Heaven (and therefore sent to Hell) is because sin makes a person unclean, and no unclean thing will enter Heaven. The purpose of Christ was to make a way for the unclean sinners to enter Heaven by clearing their slates. In this sense, it is the sin that puts someone in Hell, not the lack of belief.
However, the Bible commands us to love God with all of our hearts, so, by not believing in God, atheists are sinning by not loving God. In this way, lack of belief is causing you to go to Hell because it is a sin.
In a sense, you are right that lack of belief supposedly sends you to Hell, but the bigger picture is that it is what you do or don’t do that puts you in Hell.
For the record, I don’t believe any of this.