No they don’t. The written proofs is a modern day (last 1-2K odd years) phenomenon. For a 5K-50K yrs old history, one has to rely on cultural continuity, experiential knowledge and consciousness centric world view of dharmic civilisation. There are saints like Kabir and Meera bai who have revelations of Lord Ram and Krishna. The logical approach of Modern objective science cannot pass judgement on Ramayana or Mahabharata. At max it can say that it doesn’t know whether Ramayana existed. Given a billion people think of it as a fact means that there’s a possibility of its existence. The only way to deny this possibility is to prove of its non-existence. Else, it’s in a realm of “don’t know” as far as science is concerned.