How do we know faith is essential for entering God's rest?

According to Hebrews 4:2, the gospel was preached, but the Israelites did not enter God's rest because it was not mixed with faith. The implication here is clear: faith is the only means through which we access the rest that God promises. This teaching is pivotal in understanding that it is not merely intellectual assent to the truths of the gospel that leads to rest, but a heartfelt trust in Christ as our Savior and the sufficiency of His sacrifice. Faith is seen as a living, active trust that believes God with the whole heart, ensuring our entrance into the rest of God.