You're partially correct. Faith and belief are not synonymous however I do agree that when one considers the whole of Scripture, both are in the path to salvation. You referenced John 3:16 as the proof text for faith being required for salvation but John 3:16 does not speak of faith. Then you indicated that repentance was required for salvation and I agree but John 3:16 says nothing about repentance. I propose that you referenced the wrong verse or maybe didn't reference enough Scripture to truly support what you were trying to say.many times in the bible belief is synonymous with faith. romans 10:9 mention believing and being saved, as the only requirement for salvation. Yet elsewhere we know this believe is actually faith. Ephesians 2:8. So it contradicts and unless they have different methods of salvation, we must look at faith and belief as being synonymous to avoid contradiction in thought, and to use proper hermeneutics.
Faith is a gift from God.
So then faith comes by hearing, and hearing by the word of God. Romans 10:17 NKJV
For by grace you have been saved through faith, and that not of yourselves; it is the gift of God... Ephesians 2:8 NKJV
Therefore we also, since we are surrounded by so great a cloud of witnesses, let us lay aside every weight, and the sin which so easily ensnares us, and let us run with endurance the race that is set before us, looking unto Jesus, the author and finisher of our faith, who for the joy that was set before Him endured the cross, despising the shame, and has sat down at the right hand of the throne of God. Hebrews 12:1-2 NKJV
Believing is our reaction to the faith we have received.
Jesus said to him, “Thomas, because you have seen Me, you have believed. Blessed are those who have not seen and yet have believed.” John 20:29 NKJV
We must do the believing.
“Let not your heart be troubled; you believe in God, believe also in Me." John 14:1 NKJV
How might we be saved? By believing. That's an action on our part.
For God so loved the world that He gave His only begotten Son, that whoever believes in Him should not perish but have everlasting life. For God did not send His Son into the world to condemn the world, but that the world through Him might be saved. John 3:16 NKJV
Do you know where Scripture defines belief or believing as a gift from God or something that God inspires us to do outside of ourselves? I haven't found any yet.