All perfect praise be to Allah, The Lord of the worlds. I testify that there is none worthy of worship except Allah and that Muhammad is His slave and Messenger.
First of all, we will start with the Quran because it proved the existence of ‘Uzayr (Ezra); as Allah says (what means): {The Jews say, "Uzayr is the son of Allah"; and the Christians say, "The Messiah is the son of Allah." That is their statement from their mouths; they imitate the saying of those who disbelieved [before them]. May Allah destroy them; how are they deluded?} [Quran 9:30]
The resource books did not mention that the Jews who existed at the time of the revelation denied the existence of the one named ‘Uzayr or that they denied that the Jews said that he is the son of Allah, while they were very eager to discredit and deny the Quran, so this proves that he existed.
Ibn Hajar said in Fath Al-Baari, “Ibn Al-‘Arabi said in Sharh At-Tirmithi, 'The Jews refuted the statement that ‘Uzayr is the son of Allah at this present day and age, but this does not change the fact that it (that statement) existed at the time of the Prophet because it was revealed at his time, while the Jews were with him in Al-Madeenah and elsewhere, and it has never been quoted that any Jew denied or refuted this.'”
Also, the fact that some Jews denied that there is someone amongst them who claimed that ‘Uzayr is the son of Allah is evidence that his existence was a fact and not a claim. All this is rational evidence based on textual evidence from the Quran.
Also, there were various history books that stated that ‘Uzayr existed, and these books were still being published at different ages, and it was not known about the Jews that they objected to or denied the existence of ‘Uzayr.
What is more important for us is that you – as a Muslim – should be certain about the information that the Quran mentioned, whereas if the non-Muslim is convinced, then all the best, and if not, then what could you possibly do; Allah says (what means): {And if they dispute with you, then say: Allah is most knowing of what you do. Allah will judge between you on the Day of Resurrection concerning that over which you used to differ.} [Quran 22:68-69]
We should point out that the person who undertakes to debate with the people of falsehood should have enough Islamic knowledge to refute their misconceptions, otherwise he could be affected by their misconceptions and might go astray while he would not know.
Ibn Al-Qayyim said in Miftaah Daar As-Sa’aadah:
“Shaykh Ibn Taymiyyah, may Allah be pleased with him, when I started to report one misconception after another to him, said to me, 'Do not make your heart, when exposed to such trials, absorb it like a sponge that soaks up water (soaking up the various misconceptions that are presented to it), but let it be like an impermeable glass vessel, misconceptions pass by it but do not remain in it. Such a vessel sees the misconception with its [the vessel's] clearness but repels it [misconception] with its firmness. Otherwise, if your heart absorbs every misconception that passes by it, then, in that case, your heart becomes a settling place for misconceptions,' or as he said. So I do not see that I have ever benefited from any advice in repelling misconceptions more than I benefited from this advice, because a misconception is called as such because the truth is confused with falsehood in it, as it makes the garment of truthfulness cover the body of falsehood…”
Allah knows best.