The important thing to keep your eyes on in the work is the preface. There is something which just doesn't jibe. Origen begins by claiming that his patron Ambrose made his write the treatise:
And I know not, my pious Ambrosius, why you wished me to write a reply to the false charges brought by Celsus against the Christians, and to his accusations directed against the faith of the Churches in his treatise; as if the facts themselves did not furnish a manifest refutation, and the doctrine a better answer than any writing, seeing it both disposes of the false statements, and does not leave to the accusations any credibility or validity.
He goes on to cite the example of Jesus's silence before Pilate and then emphasizes that he doesn't want to carry out the task because it would be better to remain silence. But then the claim becomes strange. He not only reinforces again that the apology was written unwillingly:
I venture, then, to say that this apology which you require me to compose will somewhat weaken that defence (of Christianity) which rests on facts, and that power of Jesus which is manifest to those who are not altogether devoid of perception. Notwithstanding, that we may not have the appearance of being reluctant to undertake the task which you have enjoined, we have endeavoured, to the best of our ability, to suggest, by way of answer to each of the statements advanced by Celsus, what seemed to us adapted to refute them, although his arguments have no power to shake the faith of any (true) believer.
And that he only writes the work in order to prevent those weak in faith to have their faith shaken:
But nevertheless, since in the multitude of those who are considered believers some such persons might be found as would have their faith shaken and overthrown by the writings of Celsus, but who might be preserved by a reply to them of such a nature as to refute his statements and to exhibit the truth, we have deemed it right to yield to your injunction, and to furnish an answer to the treatise which you sent us, but which I do not think that any one, although only a short way advanced in philosophy, will allow to be a True Discourse, as Celsus has entitled it.
Yet a little later Origen makes reference to anomaly in his composition of the treatise (highlighted):
After proceeding with this work as far as the place where Celsus introduces the Jew disputing with Jesus, I resolved to prefix this preface to the beginning, in order that the reader of our reply to Celsus might fall in with it first, and see that this book has been composed not for those who are thorough believers, but for such as are either wholly unacquainted with the Christian faith, or for those who, as the apostle terms them, are weak in the faith; regarding whom he says, Receive him that is weak in the faith. And this preface must be my apology for beginning my answer to Celsus on one plan, and carrying it on on another. For my first intention was to indicate his principal objections, and then briefly the answers that were returned to them, and subsequently to make a systematic treatise of the whole discourse. But afterwards, circumstances themselves suggested to me that I should be economical of my time, and that, satisfied with what I had already stated at the commencement, I should in the following part grapple closely, to the best of my ability, with the charges of Celsus. I have therefore to ask indulgence for those portions which follow the preface towards the beginning of the book. And if you are not impressed by the powerful arguments which succeed, then, asking similar indulgence also with respect to them, I refer you, if you still desire an argumentative solution of the objections of Celsus, to those men who are wiser than myself, and who are able by words and treatises to overthrow the charges which he brings against us. But better is the man who, although meeting with the work of Celsus, needs no answer to it at all, but who despises all its contents, since they are contemned, and with good reason, by every believer in Christ, through the Spirit that is in him.
Of course if you accept this explanation you won't need to look any further. Yet it is important to note what Origen is really saying. The existing treatise as it is preserved now has two different 'natures' as it were. Origen first says that he had 'given answer' (ὑπαγορεῦσαι > ὑπαγόρευσις) from the beginning and the "introduction" (προοίμιον) "until" (μέχρι) the part where the Jew of Celsus" (= τῆς παρὰ Κέλσῳ τοῦ Ἰουδαίου) in a scrambled an order but followed the order of the treatise thereafter. That's strange enough (i.e. why would the nature of the treatise be different before and after the Jewish treatise). But the word ὑπαγόρευσις is very rare. I don't have access to a complete list of Greek texts. But from Perseus I see the term appears only in Josephus (7 times) and 2 times in Achilles Tatius (a writer I have never heard of before).
I doubt very much that the introduction was actually written by Origen. Eusebius would be my guess. The question of course is why.