What is the proof that Ramayana is real?

There are 2 issues involved in the question.

1.  Whether Ramayana really happened?

2. If so, what is the age of Ramayana and what are the archaeological evidences for the same?

In replying to these questions, it can be argued in either way - It did happen (or) it did not happen.  And, it can be argued in 3rd way also - it might have happened, but the core story might be somewhat different.

a)  If it is accepted based pure belief, which went deep into psyche of the believers, then the question of the archaeological evidences comes up.   If it did happen long back, say some thousands of years back (or) lakhs of years back, it is very difficult to gather the archaeological evidences.  

Many evidences might have been covered in the deep layers of the Earth.  And, after the occurrence of Ramayana, if the major civilisation got wiped out, except passing down of the EPIC orally from generation to generation like passing of Vedas, due to some unknown reasons,   it is very difficult convince.

b)  If it not accepted in the absence of the archaeological evidences,  a counter question can be posed to the non-believers.

I)     Let us assume a situation.  

The time is 2500 AD.  All the major countries existing  got involved in a major war that broke out in 2125 AD (present day Chinese ambitious programmes and ISIS threats, etc, can be a cause for the III world war) , might got eliminated and some lesser known countries were left to feed themselves, without having the know how of present day advanced technology.

They will be having the books with them to indicate happenings of I World War, II World War and III World War.

Can the remaining people belonging to those lesser known countries,    provide archaeological evidences for the happenings of   I World War,   II World War and   III World War, to their next generations?   May not.

Does it mean, those incidents might not have happened? 

II)    If the media reports about the missile guided technology developed by the USA, people  say, it is an advanced technology, which will chase the moving target till it destroys.

If I say, Sri Rama in Ramayana used missile guided technology, you say it is a MYTH.  

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Arguments apart,  let us consider  an incident that took place during the life time of Shri Shirdi Sai Baba.  I believe Saints, as they will not tell false stories.

One devotee of Shri Sai Baba was Shama. Shama was the closest of Sai Baba, and shared a relationship of a closest friend, with Saibaba. Shama would speak with Sai Baba, as a closest friend speaks, quite knowing the stature of Sai Baba.

Once the following incident took place. Shama asked Sai Baba, 

 "Deva (Shama always use to address Sai Baba by Deva, meaning God) it is written in Ramayana that Lord Rama got a bridge built by 1 crore (10 million) monkeys. This bridge (is called Setu) spanned the sea, so Lord Rama and his troops could cross the sea and reach Lanka. There He waged war with Ravana and vanquished him. Deva, is this true."

Sai Baba replied, "Yes this is true. The sea is real and Lord Rama was really there."

Shama inquired, "Deva, where did so many monkeys sit? And how did they sit?

Sai Baba replied, "They sat on the trees and clung to the branches. They looked like myriads of ants."

Then Shama asked Sai Baba, which perhaps only he could lovingly dare, "Did You see this with your own eyes?"

Sai Baba replied, "Yes, yes I saw them with my own eyes. Alright Shama."

Shama again said what only he could lovingly dare, "When I first saw You, You hardly had a stubble of mustache (a popular way in India to suggest youngsters). Then how and when did You go to see 'Vanar Sena(troops of monkeys) Re.' "

Sai Baba replied, " Shamyaa (as He lovingly called Shama) you and I have been together for many generations. I remember them but you do not."

In wonders Shama asked, "How old were You then?"

Sai Baba, "Just as you see me now."

Shama could not grasp the immensity of this spiritual fact or truth. He persisted, "Is this really true?"

Sai Baba as always, "Have I ever lied sitting here in the Dwarkamai? What I say is true. I swear by you."