Bhagavan Sri Ramachandra is Parabrahman Parmatama himself, who descended on earth for the fulfilment of wishes of his devotees.
राम भगत हित नर तनु धारी। सहि संकट किए साधु सुखारी॥
For the welfare of his devotees Rama descended in human form. He took away all miseries and gave bliss to Sages and devotees. - Balkanda, Ramcharitmanas.
There are many instances in various scriptures which shows he is Paranrahman himself, starting right from Valmiki Ramayana. The Devotees like Devi Ahilya, Devi Shabari, Maharishi Valmiki, Mahrishi Shanbhag, Suteekshna, Vashishtha, Vishwamitra, Kevat, Mahrishi Parshuram, Hanuman Ji saw Parabrahman in him.
Bhagavan Shiva always meditates on him, as Bhagavan Rama is Parabrahman himself. Not only this, every Soul is initiated with the name Rama, as this name is verily the Parabrahman and synonymous with ‘OM'.
If someone is not initiated formally by a Guru, chanting of Name Rama and worshipping Bhagavan Shri Rama with Tulsi (Sri Rama Poojanam Vidhi)/ will yield great results. - Agastya Samhita.
There are many people who have visualised Bhagavan Shri Rama's Adwitya Roopa, right from his contemporaries to his devotees in Kaliyuga Like Goswami Tulsidas and Ramadasa.
Contemporaries of Lord Rama
The very first instance where Sri Rama is seen as Parabrahman comes in Balakanda, where Devi Ahilya was liberated by him. She had a curse that she will be freed Only when Bhagavan Rama will show him to her.
When that unassailable son of Dasharatha, namely Rama, arrives at this squalid forest, for it will be henceforth rendered so along with you, then you will be purified. [1-48-31]
Even that great-resplendent Gautama is heartened when he reunited with Ahalya after a long, long a time, and that sage customarily reverenced Rama for actualising his solemn utterance, and that great-ascetic Gautama continued his ascesis together with Ahalya. [1-49-21] - Balkanda.
These words reflect the immense respect they had for Bhagavan Rama. Sage Gautama is not any ordinary sage, he is very realised soul but here he specifically greets Bhagavana for making his words true, this itself shows that Bhagavan planned all leela for the liberation of Ahilya and sanctifying Gautama's words.
Next, and a Very major instance comes when Mahrishi Parshurama encounters Bhagavan Sri Ramachandra. He stops their journey and asks Bhagavan Rama to prove himself. It was his way to ascertain whether Bhagavan, Parabrahman himself have come or not and after Sri Rama aims arrow with Vaishnava Dhanusha, this is what Mahrishi Parshurama says to him:
I have realized your touch of nature as that of the Immutable Supreme Being, God of Gods, the Exterminator of the demon Madhu, namely Vishnu, by the touch of your handling that bow... oh, enemy-inflamer, blessedness alone betides you... [1-76-17]
All of these gods who have come collectively are beholding you and your next move, for you are an unequalled one in your achievements and to whom there is no counter-dueller in conflicts... [1-76-18]
Oh, Kakutstha Rama, you are the lord of the triad of worlds, such as you are, you faced me down, and it is malapropos to say that this is a disgrace to me... [1-76-19]
These sages saw the Parabrahman in Manushya Dehdhari Bhagavan Rama, the Parabrahman who enchants the hearts of his devotees by his Leela on earth.
Another major incident of him being the Paratatva comes when Mahrishi Sharbhanga and Shabari Devi worship him, dedicating all their actions to him and attaining the most superior regions. Now , If someone is attaining the greatest regions by dedicating all their actions to Bhagavan Rama, it itself speaks of his greatness, him being the Supreme power of the universe.
On knowing that you are course is nearby, oh! Manly-tiger, and without seeing my dear guest I do not wish to go to Brahma's abode... [3-5-29]
Having met with you, a virtuous one and a great soul as you are, oh, manly-tiger, I wish to go through undesirable lesser heavens to Brahma's abode, the highest [3-5-30]
Oh! Tigerly-man, non-diminishing are the abodes achieved by me either in Brahma's abode or yonder than paradise...you take them all...that are mine achieved by me ascesis..." So said Sage Sharabhanga to Rama.
Something of similar nature is said by Devi Shabari to him, who was her deity since countless years.
"Just now, on your pleasing manifestation before me my ascesis is accomplished, and now only my birth is fructified, and now only my subservience to my mentors is well hallowed... [3-74-11]
"Oh, best one among men, now all my ascesis is fructified when I personally worshiped you, who are none other than the best god among gods, thus the heaven will also be there for me... [3-74-12]
These are words of all the sages to him, the one who is the base of the Universe.
Rama- The one who is beyond everything.
Another instance which shows that he was Parabrahman comes from the fact that he was controller of everything.
He was in the act of teaching humans when he came on the earth. For this, he tried to show how humans feel , how should they act in any situation. Valmiki Ramayana is not a simple text, even the words like ‘is', ‘are' depict great meanings in the text. It is to be read deeply to find the essence. The more you read, more and more dimensions you find to it.
Coming to question, Lord Rama used to summon the feelings. He showed feelings. He felt pain, he felt happy, he felt sadness and everything but he was not under the control of feelings, he was the controller of feelings. While fighting with Khara, he called wrath and adopted the mask of wrath.
Rama stretched his awesome bow to examine the taut of bowstring, and even whipped arrows out of quiver, and then adopted a mask of (summoned) extreme wrath to eliminate all the demons. [3-24-33]
This shows how he used to be in charge of all feelings, which all he called for the fulfilment of his purpose.
Rama Nama is Pranavakshra itself.
The name of Bhagavan Sri Rama is Pranava ‘OM' itself. The name of Bhagavan Rama becomes Trimatra like OM when deciphered with grammar rules as laid by Panini. The effect of chanting Bhagavan Rama is same as chanting OM.
Further, the Rama naam is equal to entire Shasranama of Bhagavana Hari. Bhagavana liberator of sins as said in Agastya Samhita:
Those Ascetics and Sanyasi who worship Bhagavana Sri Rama as Parabrahman eternally become free of sins and the unmindful sins do not obstruct them.
Parabrahman, As worshipped by Bhagavana Shiva and Brahma Deva.
Towards the concluding part, here I will present what Bhagavana Shiva says about Bhagavana Rama:
राम ब्रह्म ब्यापक जग जाना। परमानंद परेस पुराना॥4
Sri Rama is the Parabrahman which exist etereternally is the supreme ecstatic bliss, the ancient one and Paratatva. - Ramcharitmanasa.
Fair-faced lady (Parvati) ! My mind enjoys saying Rama Rama।
Uttering once the name of Rama is equal to the uttering of any other name of God, a thousand times॥38॥ - Rama Raksha Strotra.
After Ravana Vadh, all Deities come to worship him and Brahma Deva sings a Stuti for him. This is what he says to him:
The entire cosmos is your body. The earth constitutes your firmness. Fire is your anger. The moon constitutes your placidity. You are Lord Vishnu (who bears the mark Srivatsa - a curl of white hair on his breast)."
You are the sacrificial performance. You are the sacred syllable 'Vashat' (on hearing which the Adhvaryu priest casts the oblation to a deity into the sacrificial fire). You are the mystic syllable 'OM'. You are higher than the highest. People neither know your end nor your origin nor who you are in reality."
You are the leader of the army and the village headman. You are the intellect. You are the endurance and the subduer of the senses. You are the origin and the dissolution of all, Upendra the Divine Dwarf and (the younger brother of Indra) as also the destroyer Madhu, the demon - Valmiki Ramayana
The same is explained by Mata Sita to Hanuman Ji where she tells him how she is the Mool Prakriti and Bhagavana Rama is the Parabrahman. He is one who stays in entire universe, in every jeeva being their Atma. He stays in the heart of Shri Hanuman Ji in his Sookshma roopa. He came in material form for his Bhakta Tulsodasa asking innocently for the Chandan, he gave his vision to his Bhakta Ramadasu and he only stays eternally at Bhadrachalam. It was by power of Bhagavana Rama that Hanuman Ji could fly over to Lanka and come back safely, due to his power the fire couldn't touch him.
Concluding by the chaupai by Sage Tulsidas(Words of Bhagavana Shiva):
*राम अतर्क्य बुद्धि मन बानी। मत हमार अस सुनहि सयानी॥
तदपि संत मुनि बेद पुराना। जस कछु कहहिं स्वमति अनुमाना॥2॥
भावार्थ:-हे सयानी! सुनो, हमारा मत तो यह है कि बुद्धि, मन और वाणी से श्री रामचन्द्रजी की तर्कना नहीं की जा सकती। तथापि संत, मुनि, वेद और पुराण अपनी-अपनी बुद्धि के अनुसार जैसा कुछ कहते हैं॥2॥
Listen O Parvati! By Mind, intellect and speech one can not comprehend Bhagvana Sri Rama yet Sages, Ascetics, Vedas and Purana speak about him as per their intellect.
Jai Sri Ramachandra!