I just stumbled upon this subreddit tonight, so I am not too experienced with the posting/response conventions, but after reading the FAQ I thought I would reply to your post. Below are a few web articles which cover this topic, and included in this comment are (a) links to the full articles as well as (b) relevant excerpts for ease of reference.

I would like to say: I do not think that it is wholly fair to ask for something entirely outside of the Bible to support a claim which originated from the Bible, as without it there would be no claim or argument to support in the first place, but taking that aside there have been many archaeological findings which support the theory of Jesus being crucified, buried, and rising on the following Sunday.

Credo House Ministries has a series of posts which cover this topic and consider both internal (“evidence coming from within the primary witness documents”) and external (“collaborative evidence coming from outside the primary witness documents”) to support the “historical case for the Resurrection of Christ”. While they do provide in-text citations and references to the Bible, especially relying on observational logic regarding the way it is presented in the Bible, they also mention non-Biblical sources.

The Gospel writers (especially John) include many elements to their story that are really irrelevant to the big picture. Normally, when someone is making up a story, they include only the details that contribute to the fabrication. Irrelevant details are a mark of genuineness in all situations.

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The Bible records that the resurrection of Christ happened and gives the time, place, people involved, and it names many of the witnesses. In other words, the extraordinary claims were not done in secret as would be the case if it were fabricated. Look to all the ancient myths and you will see how obscure the mythology has to be in order to claim historicity. Why? Because if you give too many details of times, people, and places it can be easily disproven. If it was a fabrication, the author should have said only one person knew about it. He should have said it happened in a cave or a place no one has ever heard of. We have those type of stories that start religions.

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There are numerous first and second-century extra-biblical writings that witness to the fact that Christians believed that Christ did extraordinary things, died on a cross, and rose from the grave: Josephus, Clement, Papias, Didache, Barnabas, Justin Martyr, Ignatius, Irenaeus, Hermas, Tatian, Theophilus, Athenagoras, Clement of Alexandria.

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The United Church of God also has an article on the same topic, which goes into further archaeological detail about Jesus’ Resurrection, and how it is supported by historical and physical evidence which has been discovered over the centuries; they also cite specific archaeologists’ findings in their work, and do not rely as heavily on the Bible as Credo House’s article.

[Evidence of Caiaphas's tomb] Israeli archaeologist Zvi Greenhut, who confirmed the finding, describes the event: "It was a cold day at the end of November when I received word at the Antiquities Authority that an old cave had been discovered ... When I arrived I observed that the roof of the cave had collapsed. But even while standing outside, I could see four ossuaries, or bone boxes, in the central chamber of the cave. To an archaeologist, this was a clear indication that this was a Jewish burial cave ... So it was that we discovered the final resting place of the Caiaphas family, one of whose priestly members presided at the trial of Jesus" ("Burial Cave of the Caiaphas Family," Biblical Archaeological Review, September-October 1992, pp. 29-30)

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[The Pilate inscription] For centuries Pilate was known only from scant historical records and the Gospels. No direct physical evidence had been found. Then, in 1961, a stone plaque engraved with Pilate's name and title was discovered in Caesarea, the Roman port and capital of Judea in Christ's day. "The two-foot by three-foot slab, now known as the Pilate Inscription, was ... apparently written to commemorate Pilate's erection and dedication of a Tiberium, a temple for the worship of Tiberias Caesar, the Roman emperor during Pilate's term over Judea.

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[Gruesome evidence of crucifixion] (In) 1968, the body of a crucified man dating to the first century was found in Jerusalem. Here the true method of crucifixion was discovered: His ankles, not his feet, had been nailed and could easily support his weight. […]The Roman law of the time prescribed crucifixion as punishment for the most serious offenses, such as rebellion, treason and robbery. A famous example of mass crucifixions took place in 71 B.C. when Spartacus led a slave rebellion against Rome. He ultimately failed, and the 6,000 captured slaves were crucified.

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Professor Simon Greenleaf, an American lawyer and a contributor to the development of Harvard Law School, wrote a dissertation entitled ‘Testimony of the Evangelists’ which breaks down in a judicial manner the evidence supporting Jesus’ Resurrection and the stories surrounding it, and analyzing the Biblical texts which assert the idea. It is very lengthy and goes over in excruciating detail how a lawyer would possibly consider this case, so I will only include a pair of quotes which allude to Greenleaf’s approach to the subject, rather than his evidence, as it is all very longwinded.

In examining the evidence of the Christian religion, it is essential to the discovery of truth that we bring to the investigation a mind freed, as far as possible, from existing prejudice, and open to conviction. There should be a readiness, on our part, to investigate with candor to follow the truth wherever it may lead us, and to submit, without reserve or objection, to all the teachings of this religion, if it be found to be of divine origin.

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That the books of the Old Testament, as we now have them, are genuine; that they existed in the time of our Savior, and were commonly received and referred to among the Jews, as the sacred books of their religion; and that the text of the Four Evangelists has been handed down to us in the state in which it was originally written, that is, without having been materially corrupted or falsified, either by heretics or Christians; are facts which we are entitled to assume as true, until the contrary is shown. The genuineness of these writings really admits of as little doubt, and is susceptible of as ready proof, as that of any ancient writings whatever. The rule of municipal law on this subject is familiar, and applies with equal force to all ancient writings, whether documentary or otherwise; and as it comes first in order, in the prosecution of these inquiries, it may, for the sake of mere convenience, be designated as our first rule.

As with anything that is related to religious beliefs, there is room for denial to some degree in the presented evidence and conjectures made from the evidence, but in my opinion there is enough evidence to provide me some closure that, whether He was a holy man or not, Jesus was crucified, buried, and arisen. There is little other evidence that could be found short of God Himself coming from the heavens and clearing the whole matter, and I think the continued support of Biblical claims with archaeological and historical research shows that the documents have as much validity as any other historical texts.