Then why do Christians go out of their way to demonstrate that there is "overwhelming evidence" that the Resurrection is a "historical fact"?
When confronted with the fact that there is no real first hand evidence to support such a claim, they then state that it is "purely a matter of faith".
Sorry, I don't buy it.
I think claims of historical or scientific evidence are mostly a Protestant phenomenon, and more specifically, mostly an Evangelical phenomenon.
Protestants, and especially Protestant movements that arose after the first wave of classical Protestantism, like to believe that their religious beliefs are rational and that they have risen above the superstitions of Rome and the Christian East. Part of the Protestant strategy for breaking away from Christian tradition was claiming to base their religion on the Bible, which was pretty effective, but put them into an uncomfortable and novel position.
If your religion is based on the Bible, it suddenly matters very much whether the Bible is reliable, whether you have the most reliable text of the Bible, and whether your interpretation of the Bible can be rationally defended. These are issues the historic churches don't have to worry about. It doesn't matter if you have the very best, most "authentic" text, as long as you have the text that is received by the Church. You don't have to defend your interpretation of the Bible from scratch, on a rational basis; if your interpretation is in line with tradition, that's sufficient. It doesn't matter if the Bible is 100% reliable, because it's not the Bible you're relying on. I have, for instance, heard Orthodox Christians explain without the slightest qualm that certain parts of the New Testament have been superseded by the Holy Canons, and despite the undeniable fact that deaconesses are scriptural, the prevalent view among Orthodox bishops is that since the Holy Fathers have allowed the order of deaconesses to die out - the Orthodox are still living in their Patristic Age - it might be rash and inappropriate to revive it.
That's not to say you don't run across Catholic and Orthodox Creationists and similar apologists, but they're relatively rare. This kind of thing is mostly a Protestant phenomenon.
On the other hand, the traditional Christian insistence on the importance of faith has been retained by the Protestants, and with their unbearable burden of proof it's not surprising that they apply it to believing what they can't explain by reason. "Faith," says Archie Bunker, "is something you believe that nobody in his right mind would believe."
I'll grant you that thinking of faith simply as believing that for which you have no evidence is a rather debased view of faith, even from a Protestant point of view, and many Protestants are quick to point that out, but there's no denying that there's a strong element of it in Protestant religiosity. (It's also present to a lesser extent in the historic churches.)
Add to that the Evangelical obsession with "cults," and with "disproving" the claims of groups like the Mormons and Jehovah's Witnesses, and you've made evidence even more important. Not that Mormons and Jehovah's Witnesses, especially the latter, don't find themselves in roughly the same position. Part of the genius of Mormonism, though, is freeing themselves from that burden to a great extent by having a living leadership that is believed to receive direct revelations, and by urging Mormons to look within themselves and see if they can't find Mormonism being confirmed by the Holy Spirit. That means that most of the apologetic and propaganda efforts of the Mormons are directed at outsiders, while Evangelicals have a constant need to direct these efforts toward their own faithful.
So, you start with a religion that carries with it an explicit burden of proof, or at least a burden of evidence, and must be defended no only in its own right, but also against the claims of others. You make your reasoned case as best you can, and to the extent your audience accepts your reason, so far, so good. Where reason and evidence fail, you resort to claiming the necessity of faith. It is, in the context of Protestantism, almost inevitable.
Of course polemics and apologetics occur among the historic churches, too, and especially within the Roman Catholic Church, which is in general more legalistic and makes a greater attempt to seem rational than the Eastern Churches. But these kinds of arguments don't carry the same sense of urgency, or strike at the heart of historic Christianity to the same extent, as they do for Protestants.
However, for the sake of discussion, let us leave alone the search for evidence, and focus on the Resurrection being purely a matter of faith. Firstly, if that is the case, then it is for Christians alone, who should not expect the rest to accept their dogma. But that is not the case, is it? Christianity claims also that it is the one true faith, that the Resurrection was a real event, and that faith that it occurred goes along with conversion. As St. Paul said, if you don't have the Resurrection, then Christianity fails. Christians must have faith in the Resurrection, and expect everyone else to do likewise.
Secondly, if it is purely a matter of faith, what is it a matter of faith FOR? What purpose does trusting that the Resurrection occurred serve for the Christian? We know that the Crucifixion definitely served to wash sin away, but the Resurrection?
Bear in mind that having faith that the Resurrection is a real event is an admission that it may also not be true, unless, of course, by "faith", the Christian is actually saying that it is a fact. In other words, the Christian is using faith and truth interchangeably. If the Christian means that he has reason to believe that the Resurrection is true, but is not certain, then the question becomes: why is it important that the Christian needs to maintain such a belief, knowing that it may not be true?
Careful how you answer this one, please.
It's a curious thing about Christianity that belief is one of the very most important aspects of it. Other religions can be dogmatic, but none of them are dogmatic with same fervor as Christianity. All the historic churches recite creeds at their worship services; some Protestants claim to reject creeds but almost invariably invest their "statements of faith" with great importance. (And here again there's that blurring of faith and truth claims that you mention.)
Christianity, almost alone among the world religions, places greater emphasis on belief than on way of life. Muslims, Jews, Buddhists and Hindus may have definite opinions about which beliefs are correct and which are incorrect, and may think it's a very important issue, but hardly any of them ever ascribe the same importance to belief as Christians.
In normative Christianity, God can and will forgive you of the most heinous sins, provided you repent. Mass murder is no real obstacle to salvation. But if you believe the wrong thing about the Trinity or the Virgin Birth, all is lost.
It's really an odd feature of Christianity, and I've heard and read a number of attempts to explain it. I've tried to explain it myself. But I can't say I've come across a really satisfactory explanation yet.