According to P.T.Daniels in The World's Writing System (1996),
"The first Indian inscription of some length found in Southeast Asia is on the stela of Vo-canh - a granite block inscribed in Sanskrit on two faces, found near the village of Vo-canh in the province of Khanh-hoa in present-day southern Vietnam. It has been assigned to the third century C.E. and either to the ancient state of Champa or to Funan. About the end of the fourth century or the beginning of the fifth, some inscriptions were written in Quang-nam, Phu-yen, and Tra-kieu in what is now Vietnam. These are Sanskrit, except for a highly significant one that uses the same alphabet but is in the Old Cham language. [...]
On the Malay peninsula, inscriptions go back no further than the fourth century, and these are in Sanskrit. In what is now Thailand (outside the Malay peninsula), the Sanskrit inscriptions found at Si Thep on the Sak River cannot be more recent than the fifth or sixth century, and are some of the earliest examples of Indian script from that territory. In the Indonesian archipelago, as Coedès says (1968:18), the Sanskirt inscriptions of Mulavarman in the region of Kutai, east Borneo, date back to the beginning of the fifth century, and those Purnavarman in the western part of Java, to the middle of the fifth century."
Sanskrit scripts in Southeast Asia therefore cannot be older than the third century CE.
Chinese scripts in (northern) Vietnam, however, could be found at a much earlier age.
An inscription at the bottom of a bronze drum found in northern Vietnam, dating to the 3rd century BC testified for an earlier entrance of Sino script into the region.
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The drum was discovered in the year of 2003, in Phú Xuyên county of the old Hà Tây province (now part of Hanoi), dating back to the second or third century B.C. The 71-cm wide and 43-cm tall drum is named Phú.
Some characters on the drum are hard to decipher because they deviate considerably from modern characters. Of the ones that could be deciphered, the characters are 重六鈞,五斤八兩,名曰富,第未十一 (Weighed 6 鈞, 5 斤, 8 兩, named Phú, ranked 11th)
There are two characters on the drum that could not be deciphered. Dr. Viet Nguyen interpreted them as pronunciation of Cửu Chân (Jiuzhen). They could be characters made to write native words, in a manner somewhat similar to chữ Nôm.
This drum could not have been made by Chinese. Nor could it have been made for export since Chinese found no use and value in bronze drums. Why then was there Sino script on it? Not a Sino script typically found in northern China, but one containing possibly native characters.
If this is true, a script similar to chữ nôm (Sino-like ideograms but depicting a non-Sino language) had existed in Northern Vietnam before the Han dynasty conquest of this area.
This also shows that names like Cửu-Chân/Jiuzhen, Giao-Chỉ/Jiaozhi were most likely native words that were transcribed into Han characters.
Perhaps, some two centuries before the conquest of Nanyue by the Han dynasty, therefore absorbing northern Vietnam into the Han empire, Sino script was already known to and used by the natives of northern Vietnam.
Some preliminary researches have suggested that the Dongsonians of northern Vietnam could have used a type of pictogram writing, similar to that Chinese script, but of different characters. However, under expanding influence of Chinese cultures, the native pictograms must have been replaced by the Sino pictograms.
References:
The World's Wring Systems by P.T. Daniels
Ancient Inscriptions on Dongson Bronze Drum by Dr. Nguyen Viet
