But how do we know the belief, the faith is true?
By works.
What would have happened if all the Apostles and disciples decided that since they were saved, all they need do is sit back and wait for Christ to come back and get them?
No, they had to do works. They had to do something. Their faith was not just belief but action.
Both/And
Salvation includes the indwelling of the Spirit of God. In Acts Paul and Silas told the jailors “Believe on the Lord Jesus Christ, and thou shalt be saved, and thy house”. That word “believe” is powerful.
When a person truly believes and trusts in Jesus they are indwelt by the Spirit of God. How would the Spirit of God not cause one to tell others and go out and do the will of God? Would the Spirit of God which directs us after we are saved cause us to “sit back and wait”? I think not. Would a person who didn’t really trust/believe in Jesus but simply mouthed the words to impress someone sit back? Probably, because the Spirit isn’t in him. It’s the fruit of the Spirit causing us to move and do, not ourselves or our fleshly nature but the Spirit within us.