It is important to differentiate between believing and receiving. Most have been taught that to believe is the end-all of salvation but scripture says that even the demons believe. What's important is the receiving.
John 1:12
Yet to all who did receive him, to those who believed in his name, he gave the right to become children of God—
John 3:16
For God so loved the world that he gave his one and only Son, that whoever believes in him shall not perish but have eternal life.
God gave His Son and we receive the Son. There's no merit for the sinner, it's all accomplished by the Lord Jesus. The Holy Spirit came and caused us to realize our sins. While we were yet sinners, He died for us. He accomplished the salvation. When He died, He proclaimed, "It is finished!" John 19:30 He came to save, and when we are willing to be saved, the matter is settled. There is no question of complete or incomplete faith.
Getting back to John 6
which is the OP we read
John 6:37
Him who comes to Me I shall by no means cast out
Since we have responded to the offer to receive, there's now only one question, "Has He cast me out?" No because He has given us rest Matthew 11:28 and He has given us what He gave to the woman at the well
John 7:37
If anyone thirsts, let him come to Me and drink
This is the Lord's invitation. It's not just our faith that saving us, it's His grace and faithfulness. So.. Rejoice that your names are recorded in the heavens Luke 10:20 That is the glad tidings, the good news, the gospel, in a nutshell. What we keep hearing is that something else needs to be done. It's not true. What is the inheritance to be received at this time except for peace and joy. That is the promise!
Knowing that our life is hid with Christ in God can only prompt us to
set our mind on the things above. That's cause for joy and peace and gives a song to the heart.:amen: