Many Western scholars and Indian scholars with Western mindset tried to fix the age of Srimad Ramayana, to approximately the 5th to 4th century BC. And, they succeeded to some extent in making people believe in the above fictitious theory.
If we study Srimad Ramayana in depth, we will get a clue to this riddle.
After conquering Lankhini, the Godess of Lanka, Sri Hanuma enters Lanka and searches for Seeta. Sage Valmiki describes what Sri Hanuma saw, as follows:
त्रिविष्टप निभम् दिव्यम् दिव्य नाद विनादितम् |
वाजि हेषित सम्घुष्टम् नादितम् भूषणैः तथा ||
रथैः यानैः विमानैः च तथा गज हयैः शुभैः |
वारणैः च चतुः दन्तैः श्वेत अभ्र निचय उपमैः ||
भूषितम् रुचिर द्वारम् मत्तैः च मृग पक्षिभिः |
राक्षस अधिपतेः गुप्तम् आविवेश गृहम् कपिः ||
The great Hanuma entered secretly Ravana's inner city which was equal to paradise, rendered noisy by neighing of horses and tinkling of ornaments, by chariots, vehicles and aerial-cars and decorated by auspicious elephants and horses and great elephants with four tusks and by birds and animals in heat. It had beautiful entrances and was protected by thousands of rakshasas with great strength.
(Sundara Kanda 4th Sarga 26 - 28 Slokas)
उत्तमम् राक्षसावासम् हनुमानवलोकयन् |
आससादाथ लक्ष्मीवान् राक्षसेन्द्रनिवेशनम् ||
चतुर् विषाणैर् द्विरदैः त्रिविषाणैः तथैव च |
परिक्षिप्तम् असम्बाधम् रक्ष्यमाणम् उदायुधैः ||
Thereafter, Hanuma the glorious one neared and observed the best residence of Rakshasas and the house of Ravana, containing elephants with four tusks and also those with three tusks, those with two tusks and still not crowded. It was protected by soldiers bearing raised weapons.
(Sundara Kanda 9th Sarga 4 - 5 Slokas)
Here, Sage Valmiki describes elephants with four tusks and also those with three tusks and those with two tusks.
Modern anthropologists say that elephants with four tusks existed 12-1.6 million years ago.
The Gomphotheriidae were a diverse taxonomic family of extinct elephant-like animals (proboscideans). Referred to as gomphotheres, they were widespread in North America during the Miocene and Pliocene epochs, 12-1.6 million years ago. Some lived in parts of Eurasia, Beringia and, following the Great American Interchange, South America.
Gomphotheres differed from elephants in their tooth structure, particularly the chewing surfaces on the molar teeth. Most had four tusks, and their retracted facial and nasal bones prompt palaeontologists to believe that gomphotheres had elephant-like trunks.
Hence, we can infer that Srimad Ramayana was written 16 lakh or 1.6 million years ago and not 5th to 4th century BC, as the scholars made us believe.