When did the jw's first start saying that?
Probably from the beginning. That phrase is exclusively an OT command. The WT refuses to preach on the new command in the new testament to go to Jesus instead. Jesus is the reason people were waiting in the OT!
Over 400 times in the OT it mentions the phrase, "thus saith the Lord"; but that phrase is not in the NT even one time. However, 135 times the NT records Jesus saying "I say unto you". The NT nevers counsels to wait on Jehovah!
The reason the WT constantly advises to "wait on Jehovah" is because biblically it is a waste of time. They refuse to go to Jesus as directed. JW's are among the most disobedient people on earth.
Matthew 11:28
Come to me, all who labor and are heavy laden, and I will give you rest.
Matthew 11:28-30
Come to me, all who labor and are heavy laden, and I will give you rest.
Matthew 19:14
But Jesus said, “Let the little children come to me
John 14:6
Jesus said to him, “I am the way, and the truth, and the life. No one comes to the Father except through me.
Luke 18:16
But Jesus called them to him, saying, “Let the children come to me,
Luke 13: 34
“O Jerusalem, Jerusalem! The city that murders the prophets. The city that stones those sent to help her. How often I have wanted to gather your children together even as a hen protects her brood under her wings, but you wouldn’t let me.
John 14:14
If you ask Me for anything in My name, I will do it.
Philippians 2:9 KJV
“Wherefore God also hath highly exalted him, and given him a name which is above every name.”
Matthew 28:18-20
“And Jesus came and spake unto them, saying, All power is given unto me in heaven and in earth.
John 6: 37
All that the Father giveth me shall come to me; and him that cometh to me I will in no way cast out.