No, God doesn't need to hear us to know we believe. Yet there is Romans 10:9-10:
9 that if you confess with your mouth the Lord Jesus and believe in your heart that God has raised Him from the dead, you will be saved.
10 For with the heart one believes unto righteousness, and with the mouth confession is made unto salvation.
God wants us to do this, so we should.
He also doesn't need to hear us pray to know our hearts, but he tells us to pray.
Romans 10:9-10 is not in the context of conversion, it's in the context of Christian living. There are two parts there:
believe unto righteousness
confess unto salvation
being made righteous, and being saved, are not the same thing. Jesus said "If you confess Me before men, I will confess you before My Father." He also said "If you're ashamed of Me, I'll be ashamed of you"
Interestingly, the confessing Him is in the context of persecution (Matt 10:32-33)
And Him being ashamed of some will be at His coming (Luke 9:26)
This shame is also mentioned in Romans 10:11
It's also mentioned in 1John, chapter 2. Verse 23 mentions confessing the Son, and verse 28 says that we will have confidence when He is revealed, and not be put to shame
It's an eschatological salvation, not conversion
So, what would you tell someone who was asking you how they should repent and how they can believe?
First, I try to dispel the notion that repenting is doing, because the Greek word means to have a change of mind
Then I explain that we don't "do" anything. Jesus has already done it. That if he/she has confidence that Jesus has accomplished it, and are fully assured that His death and blood are sufficient for redemption and eternal life, scripture calls that belief - the same as in John 3:16. spelled out in Romans 4:21-24