As Bart Ehrman has pointed out (and as is recognized by every serious Christian and acknowedged by every study Bible), we do not have the originals of any New Testament book. And there is very good reason for this.
They were written originally on papyrus. If you don't know what that is, think about a very flimsy sort of reed, many of which were laid crosswise to one another and then beaten until they meshed. Now, the resulting sheet or scroll--on which a letter of Paul or a gospel account by Luke was written--was passed around from town to town among the early followers of Jesus (and also, thankfully, copied many times). Such papyri (and also the alternative "stationery"--dried animal skins) were not made to last for twenty centuries.
But we don't have the originals of any ancient documents.* And so the question--with regard to the reliability of documents from this period is not "Do we have the originals?" Rather, the pertinent questions are "How many copies do we have?" and "How short is the time that passed between the writing of the originals and the copies that survive?"
If we look at other ancient documents from about the same time period, the average number of surviving copies is about 20, and the average time interval (between the original and the earliest extant copy) is 1000 years. For Thucydides' History and Tacitus' Annals, for example, we have 8 and 20 copies, respectively, the earliest for each being 1,000 years after the autograph. And historians deem these to be reliable transmissions of what the originals said.
The attestation for the New Testament overwhelmingly surpasses all other ancient writings. We have over 5,000 Greek manuscripts containing part or all of the NT, plus more than 8,000 early Latin translations and thousands of others in Syriac and Coptic. A fragment of John 8 is dated at AD 117-138, within a few decades of the original. We have significant portions of other gospels from AD 200 and 250, and a copy of the entire NT that dates to AD 340!
On the two criteria used to assess the reliability of ancient documents, the New Testament in general and the gospel accounts of Jesus' life in particular enjoy an embarrassment of rich support. We can be extremely confident that we know what the originals said, even though none of the originals themselves have survived.
* A little reflection will lead you to realize that the vast majority of what you accept as true and reliable comes to you not through any original writing. Rare exceptions would be the hand-written love letters sent to you by your spouse or the post cards mailed from Mom and Dad. But the newspapers, magazines, internet articles, and virtually everything you trust to tell you the truth are not the autographs or original writings about the events in question.