This chapter of Ramayana narrates the meeting of Garuda with Rama.
न च कौतूहलं कार्यं सखित्वं प्रति काङ्क्षिणा ।
कृतकर्मा रणे वीर सखित्वं प्रतिवेत्स्यसि ॥६-५०-५७
"O, hero! You need not be so curious to know the casue of my friendship. You will know of it, once you have accomplished success in battle."
This implies Rama was not aware of his avatar.This might be because Ravana could only killed by human.
But this chapter from Rudra Samhita Section of Shiva Purana (Pg 388) narrates story of Sati meeting Rama.
On seeing Sati in guise of Sita, Rama the scion of Raghu's race repeated the name Shiva, realized the truth and laughed. He bowed to her and said
"O Sati,Obeisance to you. Where has Shiva gone? Please tell me affably.How is that you come here alone without your husband?"
"O goddess Sati, Why have you cast off your own form and assumed this guise? Take pity on me and tell me the reason thereof ".
- On hearing the words of Rama,Sati was stunned.Remembering Siva's words and realizing the truth of same she felt ashamed.
This implies Rama was aware of His avatar.
Also this answer says
Yoga Vashishtha, the text which states conversations between Vashistha, a rig vedic teacher, and various Gods and Kakbhushubdi, a creature which stands outside of normal time and sees all. It recounts the cyclical nature of time, where Kakabhushundi has seen Ramayan 11 times with different outcomes and seen Mahabharat 16 times with different results, but, after seeing Daksha Yagya twice, he did not either care to see it again or saw no point to seeing any more, as it ended the same way each time.
It says Ramayana happened 11 times and outputs were different each time. So we can presume Rama who met Sati to be Rama of earlier yugas, not Rama of 24th Treta Yuga. But the serial Devon Ke Dev Mahadev says they met Rama by travelling to future. So, according to this serial, they went from Swayambhuva Manvantara of Pitri Kalpa to 24th Treta Yuga of Vaivastara Manvantara of Swetha Varaha Kalpa.
- If we assume that Rama,who met Sati,was aware of His avatar and Rama of 24th Treta Yuga was not aware of his avatar, then why it was written in Shiva Purana Rama, scion of Raghu's race.?
- Does that mean Rama will always take birth in Raghu's Race?
- Or was chapter of Shiva Purana misinterpreted?
Without considering above questions,
- Did Rama of 24th Treta Yuga know that he was Avatar of Vishnu?