Facing the threat of execution, the speakers make a clear declaration of absolute faith. They draw a sharp line between the God they serve and the gods of the surrounding nations. While the gods of other nations are entirely powerless to save their followers, the God they worship truly exists and possesses the active power to intervene [מצודת דוד, ביאור שטיינזלץ]. He is fully capable of rescuing them from absolutely any trouble that may happen to them [רש"י].
The immediate danger is a burning fiery furnace, but the threat extends beyond the flames. They declare that God will save them directly from the hand of the king. This means that no matter what type of judgment the king decrees, or what alternative method of execution he might choose to use against them, God has the power to deliver them [מצודת דוד, יוסף אבן יחיא].
This bold statement about God's absolute ability to save them from any threat serves a crucial purpose. It lays the necessary groundwork for the rest of their message. By first establishing that God has the complete power to rescue them, they make their final position even stronger: their loyalty to Him remains absolute, even if He ultimately chooses not to save them [יוסף אבן יחיא].