Steve Hays recently wrote a post about the deity of Christ and the significance of Christianity's prevalence in the world. I want to supplement his comments by noting that modern prophecy fulfillment is a form of evidence for Jesus' divinity. And since it's modern evidence, it's not susceptible to some of the criticisms often brought against appeals to the gospels and other ancient sources. Jesus' fulfillment of the opening verses of Isaiah's Suffering Servant prophecy is an ongoing phenomenon. Even some of the initial stages of it, in the earliest centuries of Christianity (in which we have evidence for the simultaneous rejection of Jesus by most Jews and his widespread and rapidly growing influence on the Gentile world, including Gentile rulers), involves post-Biblical evidence that's significantly less susceptible to some of the objections critics cite against the Biblical documents. Some of the Old Testament passages Jesus has fulfilled, like Isaiah 9:1-7 and the Suffering Servant prophecy, are most reasonably taken as referring to a figure who's God. Jesus' fulfillment of such prophecies, part of which has occurred in the post-Biblical era, is evidence for his deity. We can make a strong case for the deity of Christ from Old Testament prophecy, without relying on Jesus' statements recorded in the gospels, Paul's teachings about Jesus' divinity, etc.
For more about the kinds of prophecies I have in mind and references to the deity of the person who fulfills the prophecies in some cases, see here, here, here, and here. Notice how these prophecies largely involve the figure's prevalence in the world and in history, which dovetails with what Steve wrote about in his post linked above.