I would like to ask about the history of the Arabic Language. When it came into existence and when it became a written language. Did it start in El Sham or another part of the world?

Praise be to Allah, the Lord of the World; and may His blessings and peace be upon our Prophet Muhammad and upon all his Family and Companions.

1) The Arabic language is one of the Semitic languages. Specialists in the science of comparative languages believe that the Arabic language is nearest to the mother language from which all Semitic languages emanated. This preservation of Arabic is due to: (1) Arabs' perpetual presence in their countries, (2) rarity of immigrants and newcomers among them, (3) weakness of relations between Arabs and other nations, and (4) lack of intermarriage and social relations with other nations.
There is disagreement among researchers in the science of comparative languages concerning who was the first to speak the Arabic language.
It was said that Adam () was the first to speak Arabic; it was said that Jibreel (Gabriel) () taught the Arabic to Noah () and then Noah taught it to his son Sam . Later, other Semitic languages emanated from it.
After a great confusion in tongues, it was said that Jurham and Qatora sons of Qahtaan Ibn 'Amer Ibn Shalih Ibn Arfakhsheed Ibn Sam Ibn Noah , were the first people to speak the Arabic language, according to al-Hafiz in his book al-Fat-h from Ibn Is-haaq .
Also, it was said that the Amalekites (giant people) were the first people to speak the Arabic language. It was said that Ya'rub Ibn Qahtaan was the first one who spoke the Arabic, so it was named after him.
It was said that Ismael (peace be upon him) was the first to speak the Arabic language that we use today. This last opinion is based on the Prophetic Hadith that reads: " Ismael was the first one who spoke plain Arabic, he was 20 years old" . This Hadith is mentioned in al-Qurtubi's Tafseer. al-Hafiz in al-Fat-h said this Hadith was reported from al-Zubair Ibn Bakkar .
But, the above-stated opinion is refuted by the traceable Hadith of Ibn Abbas concerning the story of Umm Ismael : "And he ( Ismael ) learned the Arabic from them (some tribe)" [Reported by Imam al-Bukhari ]. al-Hafiz said in al-Fat-h: 'This indicates that the tongue of his parents was not Arabic. Then, this narration shows the weakness of the opinion of those who believed that Ismael was the first to speak the Arabic language' .
And al-Hafiz brought the two opinion into agreement saying: ' Ismael was the first who spoke the plain and pure Arabic after he had learned its fundamentals from Jurhum , or it might be that Ismael was the best one among his brothers in speaking pure Arabic' .
al-Qurtubi commented on the above difference saying: 'The sound opinion is that Adam among human beings was the first to speak various languages' . The Holy Qur'an states this clearly: {And He taught Adam all the names (of everything), …} [2: 31].
No doubt that languages are full of names. In other words, Arabic is one of them since languages are included in the concept of names.
This is also proved in the Sunnah: "Allah taught Adam all the names of everything even al-Qas'ah (a large dish) and al-Qusai'ah (a small dish)" .
In reality, the Arabic language that we speak today is the same language that was used in the Arabian Peninsula and the nearby countries for a long time before the Prophetic Mission of Muhammad (Sallallahu Alaihi wa Sallam).
So, it is difficult to state a clear and precise origin of the time and place of the Arabic language. But, for sure, it is one of the Semitic languages. Here, we give preponderance to the saying that states: Allah, The Exalted, taught it to Adam when He taught him all the names of everything.
2) As for the time in which the Arabic language became a written language, we state that there is a vast disagreement concerning this point.
It was said that Idrees (peace be upon him) the first one to write in Arabic as recorded in biographies and some books of Tafseer (interpretation of the Qur'an) as al-Qurtubi , and Idrees is the son of Yard Ibn Mahael Ibn Qinoon Ibn Yanshir Ibn Shaith Ibn Adam (peace be upon him). They added that he was the first to use the pen and study arithmetics and stars.
al-Balazri in his book Futuh al-Buldaan, while mentioning the first people who started to write in Arabic, said: ' Murara Ibn Murra , Aslam Ibn Sidra and Amer Ibn Jadraa came together and drew up the (Arabic) script depending on the comparison with the Syriac inscription.
Then, some people of al-Anbaar (a place in Iraq) learned such script. In addition, Bishr Ibn 'Abdul Malik al-Kindi al-Sakoni , the Christian, a chief of Dawmat al-Jandal, used to visit al-Hira (a place in Iraq) where he learned the handwriting. And when he visited Makkah for some private concern, Sufian Ibn Umayyah Ibn 'Abd Shams and Abu Qais Ibn 'Abd Manaf saw him (i.e. Bishr) writing, so they asked him to teach them. Thus, he taught them the rules of spelling and handwriting. After that, Bishr and Sufian visited al-Taef (a place near Makkah) for business and the people of al-Taef learned the writing from these two people. Finally, handwriting becomes widespread in Makkah, al-Taef, and then, in other Arab countries'.
According to the above-narration, the Arabic script came out in al-Anbaar and al-Hira, not al-Shaam.
Other narrations state that the Arabic inscription came out in Yemen or by Egyptian Copts.
As a result, no one can give a decisive opinion in this concern, although some narrations are traced back to Ibn Is-haaq and others.
Allah knows best.