So let's get down to this:
This is from Anonymous, “Historical and Critical Reflections on Mahometanism and Socinianism,” in Four Treatises concerning the Doctrine, Discipline and Worship of the Mahometans. London: B. Lintott, 1712. pp. 196-197. I was made aware of this text by Justin Meggitt's article in NTS on mythicism and so I sought it out for more details. This means that by the 1700s reports of Tacitus' text being interpolated were already circulating.This man having seen a collection that a learned man had published in Holland, and in which he had amassed abundance of Testimonies of some Mahometan doctors, who make honourable mention of our Lord Jesus Christ, he confidently told one of his friends, that he believed all these passages were supposititious. His friend asking him upon what proofs he found such a bold decision, Vorstius answered, that there was so great a number of Christians in Arabia, Persia, and the Indies, that ‘twas very easy to conceive they had inserted these Eulogies of Jesus Christ in the books of the Mahometans. […] There is incredible stupidity and perverseness in this judgment of Vorstius; but he has many imitators among those who defend the same sentiments with him. I know certain persons who say the same thing of what Suetonius, Tacitus, and Pliny the Younger write of Jesus Christ and the Christians. Noel Aubert de Verze, the Ecebolus of our days, had the boldness to accuse the beginning of the Gospel of St. John as supposititious; and Grotius, as well as the Racovian Catechism, advanced that the word of God was not to be found in the Syriac version, at the fifth verse of the ninth chapter of the Epistle of St. Paul to the Romans, although ‘tis to be found in all copies both printed and manuscript of that version, without excepting so much as one. I know of a very learned man, who, in a book wrote to confirm the truth of the Christian religion, hath maintained that the Dialogue of Philopatris, attributed to Lucian, and printed among his works, was a piece forged by the Christians.
I find it again being referenced as suspected of being a forgery in 1792 by James Hamilton, page 309 https://www.google.com/books/edition/St ... frontcover
Also here in 1791, it is labeled a forgery along with Pliny's correspondence with Trajan on Christians: https://www.google.com/books/edition/Th ... frontcover
Given it was already in debate in English literature in 1712, my bet is that it had been being debated much longer whether this passage was authentic.
As I am not particularly familiar with Early Modern High German, or Dutch, and the likes, I am rather limited to see how much farther back it goes though.