Do we have any proof of hadiths?

Assalamualaikum, i have a question please answer, in the Quran it never mentions anything about "hadiths" and "Sunnah" is not also mentioned, the word Sunnah is mentioned but it doesn't refer to "things prophet Muhammad used to do" it refers to something else, also we dont have any proof of the hadith books, the Quran never mentions the word Hadith or Sunnah, if we dont have any proof of hadiths why do we follow them? We do have proof of the Quran, it was a book by Allah, but Allah never commands us anything about "hadiths" or "sunnahs" in the Quran, and the hadith books (Sahih Bukhari, Sahih Muslim, Sunan abu Dawud ibn Majah, jamia tirmidhi) we dont have any proof like the person who wrote it where did he/she got the information or proof that Prophet Muhammad actually said these things or did those things or not? And the person who wrote it was just a normal human being and these books were written 100+ years after Prophet Muhammad (SAW)'s death, so where did they got the proof that the Prophet said or did those things?? If you have any proof or answer to my question please reply.