Proving Christianity has never been a difficult task. The evidence we have is so powerful, many die hard atheists have set out to disprove the faith, or at least examine it, only to come back with the Holy Spirit in their hearts and the name of Christ on their tongues.
But modern atheists have found brand new ways to express their stubbornness. They point out, somewhat fairly, that the burden of proof is on the one making a claim. Ironically, this itself is a claim that is just generally accepted, even by Christians. As I said, we are quite up to the task. The problem, however, is that it seems to be a one way street. When we bring evidence, the evidence itself becomes a new claim in need of proving.
By contrast, atheist claims never seem to need so much proof. They can get away with any number of unproven claims. "Paul only became a Christian because he felt guilty for killing them." "Christianity was invented as a method of controlling people." "Moses didn't actually write the Pentateuch." My personal favorite? "Jesus never existed"...
As a Christian, and especially as an apologist, I have no issue with the idea that Christians should prove our faith. I love studying and presenting the evidence for Christianity. It strengthens my own faith, it strengthens the faith of my brethren, it has the potential to bring people to saving faith in Christ, and frankly, I find a lot of it very interesting, especially when it coincides with my favorite fields of study. But there are few things I find more annoying than atheists who claim the intellectual high ground because they're skeptical of the claims they don't want to believe, only to completely absolve themselves of all burdens of proof when they make any random, unsubstantiated, easily disprovable claim.
To give an illustration of this, let's consider a simple wallet. As you reach down to pick it up, a man comes along and says "hey, that's my wallet." "That's my wallet" is a claim. You could choose to believe it and give the wallet to the man, but you could also probe a little, just to make sure you're not handing the wallet to the wrong man. "How much money is in it?", you ask. "£50", they answer correctly. This seems like enough evidence. "Lucky guess", you say. Well now you just look like you're making excuses to avoid handing the wallet back to its owner.
Now, we could extend this article by adding more proofs and comebacks to the wallet analogy, but you can do that in your own time if you're so inclined. Suffice to say for now, evidence at the very least gives credibility to the claim. Well, as Christians, we have evidence. We have general evidence for Theism, like the Cosmological argument. We have more specific evidence for Christianity, like the secular historical documentation of the ministry and death of Jesus (as well as hostile explanations for why He appeared to rise from the dead). But of course, most importantly, we have a more sure word recorded in Scripture.
At this point, atheists will scream "circular reasoning", but no. First, I'm not claiming "the Bible is true because the Bible says it's true". That would be a silly argument. However, there are scenarios in which circular reasoning is logical, simply because it is otherwise unavoidable. How do you know, for example, that you possess reasoning skills? In order to prove your ability to reason, you must use your ability to reason.
Another example is money. How do you know the money in your wallet is real? There are fake coins and fake bank notes all over the world. You may know yours is real by looking at it. It's self-authenticating. So is your passport, your driving license, a police badge etc.
Scripture is similarly self-authenticating. It's helpful to know that it is actually not just one book. Rather, it is a collection of 66 books, written by several authors, in several locations, over a span of many years. Thus, you could think of it like this: Rather than the Bible authenticating the Bible, each Biblical author affirms the others. But they do this in more ways than just saying it.
One particularly powerful example is Isaiah 53. This contains a prophecy that is quite clearly about Jesus, so much so that if you read it to someone unfamiliar with it and ask "who is that about?", the majority of them will say it's Jesus. Some Jews have even been known to reject it as New Testament stuff. That is, until they all find out it was written 700 years before Jesus was born, in their own Scriptures.
I remember discussing with an atheist once. He initially feigned openness, and went as far as to say that if any prophecy could be shown to him to have come true, he would believe. So, Isaiah 53 being my go-to, I gave it to him. He admitted it sounded like Jesus, but then said he wanted proof it was translated properly. So I showed him it was, and he switched to needing proof that the Jews used to believe it was a prophecy about the Messiah. So I showed him they did. Still not enough. He ran out of excuses at that point, but rather than admit defeat, he just left the conversation.
It is sometimes said that when all alternatives are refuted, whatever is left, however improbable, must be true. I don't necessarily agree with the reasoning, but at this point, Christianity stands quite unopposed. There are no reasonable alternatives to the resurrection of Christ. Thus, however improbable it seems, the evidence compels all reasonable minds to admit Jesus lives. You can say He was just an alien. You can say He had an evil twin. You can say He simply passed out on the cross and recovered after a nice lie down in a tomb. All of these are real explanations given for why Jesus seemed to rise from the dead. But at that point, you're not being reasonable, and your condemnation is squarely on your own head. Repent, and believe, for He has given you more than enough evidence for His claims. You have given none for your alternatives.