The oldest available Tamil book known as Tolkappiyam written by Tolkappiyan is dated to be from 300-400bc. In this book, Tolkappiyan has mentioned that the natural languages spoken by the people in the region between Venkatam and Kumari (Indian Ocean) was formalised into Tamil.
This process was done based on the Aindra grammar system which happened to be a Sanskrit grammar system. Tolkappiyan was well versed in the Aindra system. On other words, formal Tamil which we consider as the Classical Tamil was influenced by Sanskrit grammar school.
Aindra is called as Aindiram in Tamil and the word Aindra simply means from Indra as he was considered to be the founder of this system. Tolkappiyan's teacher was a person who was well versed in the 4 Vedas. This was mentioned by Tolkappiyan himself in Tolkappiyam. It also explains why Tamil starts with syllable "ka" like most of other Indian languages.
For reference, I am attaching the prologue taken from Tolkappiyam. It is indeed proud to have one of the oldest surviving language as our mother tongue.
But let's not forget the fact about how it was formalised and lets also not forget that there are approx 7000 languages in the planet and there is no evidence to say that Tamil is the oldest language in the world. It is only one of the oldest surviving language, not the oldest.
Our ancestors would have had a different language similar to Tamil or different from Tamil prior to 300-400 bc. Language used tend to change over time. Migration of various tribes into similar region is also a contributing factor. Let's be open minded about this one fact.
வட வேங்கடம் தென் குமரி ஆயிடைத்
தமிழ் கூறும் நல் உலகத்து
வழக்கும் செய்யுளும் ஆயிரு முதலின்
எழுத்தும் சொல்லும் பொருளும் நாடிச்
செந்தமிழ் இயற்கை சிவணிய நிலத்தொடு
முந்து நூல் கண்டு முறைப்பட எண்ணிப்
புலம் தொகுத்தோனே போக்கு அறு பனுவல்
நிலம் தரு திருவின் பாண்டியன் அவையத்து
அறம் கரை நாவின் நான்மறை முற்றிய
அதங்கோட்டு ஆசாற்கு அரில் தபத் தெரிந்து
மயங்கா மரபின் எழுத்து முறை காட்டி
மல்கு நீர் வரைப்பின் ஐந்திரம் நிறைந்த
தொல்காப்பியன் எனத் தன் பெயர் தோற்றிப்
பல் புகழ் நிறுத்த படிமையோனே.
vaṭa vēṅkaṭam teṉ kumari āyiṭait
tamiḻ kūṟum nal ulakattu
vaḻakkum ceyyuḷum āyiru mutaliṉ
eḻuttum collum poruḷum nāṭic
centamiḻ iyaṟkai civaṇiya nilattoṭu
muntu nūl kaṇṭu muṟaippaṭa eṇṇip
pulam tokuttōṉē pōkku aṟu paṉuval
nilam taru tiruviṉ pāṇṭiyaṉ avaiyattu
aṟam karai nāviṉ nāṉmaṟai muṟṟiya
ataṅkōṭṭu ācāṟku aril tapat terintu
mayaṅkā marapiṉ eḻuttu muṟai kāṭṭi
malku nīr varaippiṉ aintiram niṟainta
tolkāppiyaṉ eṉat taṉ peyar tōṟṟip
pal pukaḻ niṟutta paṭimaiyōṉē.
Translation of Tolkappiyam prologue into English:
Tamil-speaking land was extended between Veenkatam (Tiruppathi) on the north and ocean Kumari on the south. The spoken and written Tamil languages are the sources of his work. He extends his study on phonetic letters, word-syntax and the matter revealed there-on. He studied properly the culture of the language-people and his predecessors' conventions and wrote his work of 'linguistic knowledge'.This work does not contain any objectionable point. It has been published in the learned-court of the Nilantharu thiruvin Nediyon. Atankoott Aasaan is the name of his professor. This professor is a man of balanced virtuous character.He is well-versed in four 'Vedas'. During his presentation some raised-doubts of his professor were cleared. The work is unambiguous. The author of this work is well-versed in 'Aindiram' (Aindra). He posses sound knowledge on sea-grit word. Tolkaappiyan is a renowned sage.