However, as far as I know, we don't exactly have other written works by Caesar

That's not true. Three of Caesar's letters to Cicero have survived in their entirety, and Cicero refers to twenty-nine. The letters are the Att. 9.6a, 9.16.2-3, 10.8b. All three letters date from early 49, the first two from March and then the third from April. Stylistically there's not much doubt that the author of these three letters is the same as the author of the de bello gallico (barring book 8) and the de bello civili.

it only refers to him in the third person?

A great deal of ink has been spilled discussing the narrative and textual effect of the third person narrative in Caesar, but regardless of what Caesar was attempting to accomplish specifically, there's nothing unusual or especially noteworthy about it, except in how masterfully Caesar uses the device. While Caesar's text is the only text called commentarii that use the third person narration, our only other surviving Republican commentarius is the commentariolum petitionis, which is a very different kind of text, commentarii being a rather broad label. In historical narratives the third person narration is pretty common. Thucydides, Xenophon, and Polybius all appear as characters in their own texts, in which case they use the third person. Cicero's dialogues are written in the third person even when he's a speaking character.

I find it pretty amazing that we have the "voice" of not only a person from so far back

I'm not sure what you mean by this. We have texts with single authors far before Caesar. We've got Assyrian and Egyptian letters, we've got texts like the Story of Wenamun. Cicero's surviving corpus of letters numbers over 900 letters. Nothing about Caesar's text is special in this regard, and casts no doubt on the authenticity of the text.

which are so often attributed directly to him?

The de bello gallico and the de bello civili are not attributed to Caesar. When a philologist says that a text is attributed to an author it means that at some point, usually in antiquity, it was common to assume that it was the work of an author, but that there is either reasonable enough doubt to make that assertion uncategorically, or it can be proven textually or otherwise that the text cannot have been the work of that author. The commentariolum petitionis, mentioned above, is attributed to Q. Cicero, the purported speaker of the text. While a majority of English speaking scholars believe that it's actually the work of Q., a number of prominent German philologists contend on stylistic grounds that it can't be the work of a Republican author. The de viris illustribus, transmitted in late antiquity under the name Aurelius Victor, is pretty much universally considered to be spurious. Usually the problem with authenticity is a) style and b) lack of attestation. That's the case with the commentariolum petitionis, for example: we know that Q. wrote a lot, because other texts say so, but we don't know that he wrote that specifically. Other spurious works can be called into question when the attestation first appears long after the text has been being transmitted. Already in antiquity most of the texts attributed to Homer were already being called into question, and it's clear that most of them are of a much later date than the Homeric epics. Diogenes Laertius lists thirteen epistles of Plato, but gives no information about them, which has long caused a problem for the authenticity of the thirteen epistles surviving in the Platonic corpus. The Alexandrian scholars--two hundred years later--thought they were genuine, despite rejecting several of the dialogues for being inauthentic, but at least one of them (the First) is unquestionably a forgery and the others can at best be tentatively accepted.

To understand not only how this particular process works but also how textual criticism in general works, the standard teaching text is Wilson, Scribes and Scholars.

Caesar's text suffers from none of these problems. Cicero, who wrote his own commentarii about his consulship in 63, mentions the commentarii in the Brutus, and praises Caesar's style by name. Suetonius, by the way, quotes Cicero's comments on the text and mentions Cicero and the Brutus by name. The Brutus was probably written no later than 46. So we have a contemporary attestation of the text, which is far better than...basically literally any other text to have survived. We have no contemporary attestation of Herodotus' text. We have no contemporary attestation of Thucydides. We have no contemporary attestation of Xenophon, or Polybius, or Sallust. We have arguably more contemporary information about Caesar's text than Livy's. We have about as much contemporary information about Tacitus' text, in that we know from Pliny's letters that Tacitus was writing histories and we know from Tacitus' tomb inscription a little bit about when his political career was active. On top of this, we of course have attestation from later authors: Plutarch, Suetonius, Appian, etc. Compare a contemporary of Caesar: Cicero himself. Cicero's fourth Catilinarian oration survives in its entirety, and we know about the circumstances of its delivery from Plutarch. Sallust, who was tribune of the people when Cicero delivered the Pro Milone in 52, doesn't mention it during the so-called Catilinarian Debate in the Bellum Catilinae. In fact, he only mentions the first of the Catilinarian orations specifically. But there's no good reason to doubt that the Catilinarian orations are genuine. There's no evidence to suggest that they aren't by Cicero, and every reason to believe that they are. Caesar's text is basically the same.

Now, one might pipe up to point out that book 8 of the de bello gallico isn't thought to be by Caesar, nor are the other surviving texts of the Caesarian corpus: the Alexandrian War, the Spanish War, and the African War. In these later texts of the corpus, there's no mention in any of the ancient texts that they were by Caesar, and Suetonius specifically says that they aren't by Caesar, suggesting as authors either Oppius or Hirtius. While the author of book 8 of the de bello gallico does not name himself, he does point out that he's not Caesar, that he's appending the book to Caesar's text (so there's another contemporary attestation, unless we suppose that book 8 was added much later for some reason), and he addresses his comments to Cornelius Balbus, one of Caesar's friends. The preface of book 8 also tells us that the de bello civili was unfinished, ending with the runup to the Alexandrian War, and that the ending of the de bello gallico and the beginning of the de bello civili don't line up perfectly chronologically, so the author wants to bridge that year or so that's left out. The author also tells us that he personally wasn't at the Alexandrian or African campaigns, but he heard about them directly from Caesar. All of this points to one of Caesar's officers, or somebody doing a good job impersonating one, and Suetonius tells us directly that Hirtius wrote book 8. Hirtius may have been tribune in 48, but in any case he was probably at Rome from 48, when he left Antioch, to 46, when he was praetor. So not only is there no reason to doubt what Suetonius says, all the evidence points to Hirtius as the author of book 8.