Recently I heard that only those who have undergone samashrayanam or bharanyasam must recite Rahasya Trayam. I have neither performed samashrayanam nor undergone bharanyasam yet; but I am learning Vedas and Srimad Bhagavad Gita, through which learned about Ashtaksharam and Charama Sloka. Based on my understanding, Dvaya mantra is part of Srimad Ramayanam. I want to know whether one who has not performed samshrayanam or bharanyasam can recite Srimad Ramayanam, Srimad Bahgavad Gita, Upanisha,etc.

One can start learning the Vedas and Upanishad immediately after Upanayanam.
Males can start with Srimad Ramayanam, Srimad Bhagavad Gita, and meanings of other Mantras soon after samashrayanam.
Need not wait to start learning anything after bharanyasam.
However, these days it is a practice to teach Srimad Ramayanam, Srimad Bhagavad Gita, etc. to one right from a young age. It is better to go by the advice of Acharyas and wise men.
Notes:
One starts with Srimad Ramayanam and Srimad Bhagavad Gita as storytelling for young children. But there are rules to be followed to learn the actual meaning.