So glad you asked actually! This 8 min video gives an explanation. It may be a little technical, but it is worth it, especially at the end. It not only shows how God existed, but that we can know that it is the God of the Bible (Christ) that is the true God.
This would be good for you to watch too Doseofreality, as it pertains to our recent talks (the last minute part does).
http://m.youtube.com/watch?v=Sr5lY0TcdAw
Well, it's convincing to someone who ALREADY believes there is a God, just like Thomas Aquinas' Five Proofs of God is only convincing to those who already believe.
I will add too that while I personally believe that Jesus fulfilled the Hebrew Scriptures with His life, you could argue that the prophecies are vague and could be applied to a number of lives in the thousands of years. I have read that there is a mathematician found that that it's HIGHLY UNLIKELY, to the point of being impossible, that Jesus didn't fulfill all these prophecies.
[quotehttp://voices.yahoo.com/what-odds-jesus-700-plus-prophecies-fulfillment-5064980.html]Most scholars acknowledge that there are possibly seven hundred prophecies or more about Jesus Christ in the Bible.[/quote]
MOST. So there is some disagreement over the number. Changes the probability number.
For the sake of being able to wrap your mind around the odds, let's just take eight prophecies. The actual mathematical probability that Jesus Christ could have fulfilled even eight prophecies would still be a mind boggling 1 in 1017 of a chance! Put another way, it's 10 to the 157th power.
Yeah, WHICH prophecies? Some would be more or less probable than others, thus changing the number greatly.
Now, what are the odds that only 48 of the more than 700 [that we know of] prophecies of Jesus were fulfilled? Dr Peter Stoner [Science Speaks, 1958] estimated the odds against just 48 of the 300 or so Old Testament prophecies about the Messiah being fulfilled in one person. He calculated the odds at 1 in 10 to the power 157. [1]
Mr. Stoner does have the credentials to make this estimate - but he is also a deeply religious Christian. That would color how he reads his calculations, and results. That is just basic human psychology - our worldview affects the way we look and come to evidence. I would like to see an unbelieving mathematician do the same calculations, and see what happens.
But to a skeptic, that is not PROOF, because it is PROBABILITY, which means that there is A CHANCE, however be it small, that the prophets COULD'VE got that much right about one man by luck. Plus, some scholars may argue which prophecies can be interpreted of being fulfilled by Christ. This article throws out the number 700 AND 300. And as the article following explains, if you read the text in a historical context, as in what the OT authors meant when they wrote something vs how the NT interpreted them, it starts to look a little fishy to those who are sincere historians (in other words, they understand that ancient literature of history wasn't written in a factual way like it is today. If you want to argue the Gospels are factual right down to the letter, you would also have to assume that other ancient texts from neighboring countries were as well).
For those who want to educate themselves on an EQUALLY convincing argument ON THE OTHER SIDE, here's a link:
Probability Proves Bible Prophecy (or Not)
If you believe in Jesus, and had a religious experience, this article will mean nothing to you, and look like utter foolishness - just like the article above that one would look like utter foolishness to unbelievers. It's all a matter of perspective. Both are good arguments. If you could prove things about Jesus' existence, I assure you that the Gospels would be considered for history books. But considering the time period they were written and what we know about other works written around that time period (in other words, ancient ways of thinking) that would be a huge feat.
Don't bury your head in the sand as to why people reject the faith (I'm speaking to everyone). If you could tell someone, "Yeah, I know you probably believe x" AND you get that information from a first-hand source, you will appear like an honest listener to the person, rather than just a "soul-winner," and he/she will likely open up to hearing what you have to say.