The Malabar coast had lots of contact with Rome; Indians were seen in Alexandria in the 2nd century AD, and probably much before that. A canal connected the easternmost branch of the Nile and the Red Sea, through which ships could sail between India and Alexandria.
Many Jews are said to have settled in India after the Temple was destroyed; but most likely there were Jewish communities there much before (perhaps India was the ‘Ophir’ to which Solomon sent ships).
Thomas is said to have preached there, and a copy of a gospel in Hebrew was reported to have been seen there by a traveler in the later Roman period(IIRC).
"One legend holds that the Jews first settled in India during the time of King Solomon, when there was trade in teak, ivory, spices and peacocks between the Land of Israel and the Malabar Coast, where Cochin is located. Others put their arrival at the time of the Assyrian exile in 722 B.C.E., the Babylonian exile in 586 or after the destruction of the Second Temple in 70 CE No reliable evidence exists, but most contemporary scholars fix the date at some time during the early Middle Ages.
12th Dynasty
Perhaps as early as the 12th Dynasty, Pharaoh Senusret III (1878 BC - 1839 BC) may have had a west-east canal dug through the Wadi Tumilat, joining the Nile with the Red Sea, for direct trade with Punt, and thus allowing trade indirectly between the Red Sea and Mediterranean. Evidence indicates its existence by the 13th century BC during the time of Ramesses II.
Repair by Necho, Darius I and Ptolemy
It later fell into disrepair, and according to the Histories of the Greek historian Herodotus, about 600 BC, Necho II undertook re-excavation but did not complete it.
The canal was finally completed by Darius I of Persia, who conquered Egypt. According to Herodotus, the completed canal was wide enough that two triremes could pass each other with oars extended, and required 4 days to traverse. Darius commemorated his achievement with a number of granite stelae that he set up on the Nile bank, including one near Kabret, 130 miles from Pie. The Darius Inscriptions read:
“ Saith King Darius: I am a Persian. Setting out from Persia, I conquered Egypt. I ordered this canal dug from the river called the Nile that flows in Egypt, to the sea that begins in Persia. When the canal had been dug as I ordered, ships went from Egypt through this canal to Persia, even as I intended.”
It was again restored by Ptolemy II about 250 BC. Over the next 1000 years it was successively modified, destroyed and rebuilt, until finally being put out of commission in the 8th century by the Abbasid Caliph al-Mansur.
Many Jews in India went there around the time of the Inquisition, when the Catholic Church chased/persecuted them from/in Spain. The others have been there since eons.