There are a number of scholars from the entire range of the liberal/conservative spectrum who have said the most certain thing we can know about Jesus is that the Romans executed him by crucifixion. I don't know what all their individual reasons are for saying that, but I'll tell you what I think is the strongest reason.
The early Christians thought Jesus was the Christ. He was the fulfillment of the promises given to Israel to always have a man on the throne of David. By claiming to be the Christ, Jesus was essentially claiming to be the promised king of Israel. It was natural, then, that people would expect him to redeem Israel--to run the Romans off and reestablish Israel's national sovereignty and to usher in the kingdom of God on earth.
Now think about this. How likely is it that a group of Jews would make up a story about a christ and include in the story that the christ was killed by Israel's enemies? And they didn't even say he was killed heroically in battle. Rather, they came up with the most humiliating way for a criminal to die--by public crucifixion. And then they went about trying to win people over to this criminal-on-the-cross. I think that is an absurd notion.
If anything, I think Jesus' followers would've gone into damage control mode as a result of the crucifixion. They wouldn't have invented the idea. At worst, the idea that Jesus' died for sins was an invention meant to redeem Jesus' death on the cross. And the resurrection was invented to maintain the notion that Jesus was the christ in the face of his death.
In my opinion, the crucifixion of Jesus is about as certain as any historical event could be without having video footage. I have a hard time taking anybody seriously who denies it.
And that entails that Jesus existed, which is why I also have a hard time taking anybody seriously who denies the existence of Jesus.