There are some records regarding the first narration of the two epics-Ramayana and Mahabharata both. However, this is no exact proof of the exact origin of the narration. The theories shared so far is enough to amuse you and is a worthy read.
According to the Puranas, it was Luv and Kush, the two sons of Rama and Sita who first narrated the epic. Surprised! Luv and Kush were born in the sanctum of Sage Valmiki. At the time, when Sita went to the forest, she was pregnant. As we know, it was Valmiki, the poet, who composed the Ramayana first.
It is believed that Valmiki gave the first lesson on Ramayana to his two disciples, Luv and Kush. During their classes, both sang the epic, along with Veena (the instrument). But how did they finally narrate it?
The story goes to the time of Ashwamedha (Horse) sacrifice. After Lord Rama send his horse across the country, wondering as per the ritual, it was Luv and Kush who captured the horse and tied it. Initially, both fought with Bharata, Shatrughna, Lakshmana and then, Rama. It was now; the boys sang the Ramayana to Rama.
The surprising factor is that Rama had not heard the epic before and it was his two sons who told him about Ramayana. Rama was overwhelmed with the story. Eventually, he came to know that Luv and Kush were his sons and a whole family reunification happened.
Mahabharat, the longest epic, has been narrated in the forests of Naimisha by the sage Ugrasrava Sauti. The one who tells the story is Sauti. Ugrasrava is said to have been performing a yagna under Shaunaka Kulapati. The one who listens is Shaunaka.
Romaharshana, a disciple of Vyasa is the father of Ugrashrava Sauti. It is during the 12th century when Ugrasrava visits the Naimisha forest. He (Sauti) is a guest who has visited many places before including the Kurukshetra. On the behest of Shaunaka, Sauti first talks about Bharata, which was narrated to him by Vyasa’s disciple Vaisampayana.
Vaisampayana heard the story from Vyasa and first told the story to King Janamejaya (Pariskshit’s son and Abhimanyu’s grandson). He narrated the story during the time of King’s snake sacrifice and Ugrasrava was present during the ritual. So, Ugrasrava first heads the Mahabharata story at Janamejaya snake sacrifice. It was then compiled into 24,000 slokas and renamed Vijaya and eventually, Bharata.
After this generation, Ugrasravas, who belonged to the next generation from the Suta caste, were typically the bards (one who recites epics or carries forward an oral tradition) of Puranic literature and belonged to the Suta caste, and that he has he narrated it to Saunaka and other sages Naimisa forest.
Unable to convince at the narration of Bharata, Sauti then dwells upon Shaunaka’s forefathers, starting with Brighu. Shaunaka Kulapati is a Rishi from the dynasty of Brighu fleshing out the story, using complex and aligned layers. There were several narrations in no order.
The complete 100,000 verses of the Mahabharata were completed many centuries after and during that time, many new stories were added to it before it came to be titled as the epic ‘Mahabharata’.