"We have no New Testament Manuscript in Aramaic. The New Testament was written in Greek. If some of the original New Testament writings were in Aramaic (although there is no proof) "
We do have proof of Matthew being written in Aramaic. Not the original texts, however several of the early Church Fathers wrote of Matthew being written in Aramaic.
“Matthew compiled the sayings [of the Lord] in the Aramaic language, and everyone translated them as well as he could” Papias, bishop of Hieropolis c. 130 A.D. (Explanation of the Sayings of the Lord [cited by Eusebius in History of the Church 3:39]).
“Matthew also issued a written Gospel among the Hebrews in their own dialect, while Peter and Paul were preaching in Rome and laying the foundation of the Church. After their departure, Mark, the disciple and interpreter of Peter, did also hand down to us in writing what had been preached by Peter. Luke also, the companion of Paul, recorded in a book the Gospel preached by him. Afterwards John, the disciple of the Lord, who also had leaned upon his breast, did himself publish a Gospel during his residence at Ephesus in Asia” - Irenaeus of Lyons (Against Heresies 3:1:1).
“Among the four Gospels, which are the only indisputable ones in the Church of God under heaven, I have learned by tradition that the first was written by Matthew, who was once a publican, but afterwards an apostle of Jesus Christ, and it was prepared for the converts from Judaism and published in the Hebrew language” Origen c. 244 A.D. (Commentaries on Matthew [cited by Eusebius in History of the Church 6:25]).
“Matthew had begun by preaching to the Hebrews, and when he made up his mind to go to others too, he committed his own Gospel to writing in his native tongue [Aramaic], so that for those with whom he was no longer present the gap left by his departure was filled by what he wrote” – Eusebius (History of the Church 3:24 [inter 300-325]).