You are mostly right except that there is no contemporaneus evidence that Jesus even existed.
mohammed never existed.
You are obviously incapable of thinking like a historian. There is a vast amount of contemporary evidence shortly after Jesus’ death that something phenomenal happened as a result of this man and his ‘movement’ which was rapidly spreading throughout the Roman empire. It’s preposterous to assume that this movement for which many were prepared to die and which electrified the classical world order just suddenly emerged out of a vacuum without cause. This doesn’t prove his divinity but all agree that SOMETHING astounding happened as a result of this person “Jesus.” Even Suetonius made reference to him. By the way, the Epistles of St. Paul were written long before the Gospel and only a few years after the crucifixion. I consider Paul ‘objective’ in the sense that before his conversion he was an ardent persecutor of Christians. Perhaps you think that these Christians were a figment of his imagination and that the person responsible for their new faith was also an illusion.I could go on but, suffice to say, history, historiography, and epistemology couldn’t exist with your unreasonable mindset.