When I see this discussed I think of this verse.
“But to him that worketh not, but believeth on him that justifieth the ungodly, his faith is counted for righteousness.”
Romans 4:5 KJV
https://bible.com/bible/1/rom.4.5.KJV
Here we see a person who believes and has faith but has no works.
If you read through John 5 and 6 to this point you will find a common theme. The Father is working so that the will believe in his Son.
“Then answered Jesus and said unto them, Verily, verily, I say unto you, The Son can do nothing of himself, but what he seeth the Father do: for what things soever he doeth, these also doeth the Son likewise. For the Father loveth the Son, and sheweth him all things that himself doeth: and he will shew him greater works than these, that ye may marvel. For as the Father raiseth up the dead, and quickeneth them; even so the Son quickeneth whom he will. For the Father judgeth no man, but hath committed all judgment unto the Son: that all men should honour the Son, even as they honour the Father. He that honoureth not the Son honoureth not the Father which hath sent him. Verily, verily, I say unto you, He that heareth my word, and believeth on him that sent me, hath everlasting life, and shall not come into condemnation; but is passed from death unto life.”
John 5:19-24 KJV
https://bible.com/bible/1/jhn.5.19-24.KJV
“But I have greater witness than that of John: for the works which the Father hath given me to finish, the same works that I do, bear witness of me, that the Father hath sent me. And the Father himself, which hath sent me, hath borne witness of me. Ye have neither heard his voice at any time, nor seen his shape.”
John 5:36-37 KJV
https://bible.com/bible/1/jhn.5.36-37.KJV
“It is written in the prophets, And they shall be all taught of God. Every man therefore that hath heard, and hath learned of the Father, cometh unto me.”
John 6:45 KJV
https://bible.com/bible/1/jhn.6.45.KJV
The Father was bearing witness of the Son.
In John 6:29 Jesus was simply saying that the work of God was to persuade them to believe in Jesus by testifying to the fact that Jesus was the Christ.
“Jesus answered and said unto them, This is the work of God, that ye believe on him whom he hath sent.”
John 6:29 KJV
https://bible.com/bible/1/jhn.6.29.KJV