Is there any extra-biblical evidence for the triumphal entry of Jesus into Jerusalem?
No. There is no mention of the triumphal entry of Jesus into Jerusalem. The non-believers who mentioned Jesus and Christians only mentioned the most general facts, such as their devotion to Christ, the death of Jesus, the fact that people believed in his resurrection and his miracles. Minute details, of course, are not mentioned by non-believers who probably would not even know about these events, never mind have a reason to mention them. Let me use a comparative example. Let’s say you mentioned Mormonism to your friend. What would you say? You would say that it was founded by Joseph Smith, that he was killed in a jailhouse shoot-out, that he was famous for polygamy and that his followers went to Utah after his death. An unimportant detail such as something like the triumphal entry (for example his move from Far West Missouri to Nauvoo, Illinois, which is so important to Mormons) you would not even know about, never mind mentioning it to your friend. Or to use another example, even today, a Buddhist or an atheist would not even know about the triumphal entry, so obviously would not mention it in any conversation.