Islam is scientifically recording Quran and other related documents like hadith, biography from the time of its initiation, but the very first mention of the Muslims by a non -Western source was written on ( Doctrina Iacobi Nuper Baptizati) 13–20 AH / 634–640 CE.
Look at the very first conception of the Muslims as 'saracen':
"When the candidatus was killed by the Saracens, I was at Caesarea and I set off by boat to Sykamina. People were saying "the candidatus has been killed," and we Jews were overjoyed. And they were saying that the prophet had appeared, coming with the Saracens, and that he was proclaiming the advent of the anointed one, the Christ who was to come. I, having arrived at Sykamina, stopped by a certain old man well-versed in scriptures, and I said to him: "What can you tell me about the prophet who has appeared with the Saracens?" He replied, groaning deeply: "He is false, for the prophets do not come armed with a sword. Truly they are works of anarchy being committed today and I fear that the first Christ to come, whom the Christians worship, was the one sent by God and we instead are preparing to receive the Antichrist. Indeed, Isaiah said that the Jews would retain a perverted and hardened heart until all the earth should be devastated. But you go, master Abraham, and find out about the prophet who has appeared." So I, Abraham, inquired and heard from those who had met him that there was no truth to be found in the so-called prophet, only the shedding of men's blood. He says also that he has the keys of paradise, which is incredible"