You have stated that Matthew was there, ad nauseam, but you never showed how you know that. But that's fine, I understand it's a faith belief of yours.
For you. The way I came to the conclusion (you don't have to agree) is by the following:
1. Tertullian of Carthage (ca. 160–225; Against Marcion 4.2.1–2):
“I lay it down to begin with that the documents of the gospel have the apostles for their authors, and that this task of promulgating the gospel was imposed upon them by the Lord himself. . . . In short, from among the apostles, John and Matthew implant in us the faith, while from among the apostolic men Luke and Mark reaffirm it.”
2. Irenaeus of Lyons (ca. 130–200; Against Heresies 3.1.1–2; cf. Eusebius, Ecclesiastical History5.8.1–4):
“So Matthew brought out a written gospel among the Jews in their own style, when Peter and Paul were preaching the gospel at Rome and founding the church. But after their demise Mark himself, the disciple and recorder of Peter, has also handed on to us in writing what had been proclaimed by Peter. And Luke, the follower of Paul, set forth in a book the gospel that was proclaimed by him. Later John, the disciple of the Lord and the one who leaned against his chest, also put out a Gospel while residing in Ephesus of Asia.”
3. Papias of Hierapolis (ca. 125 AD, Recorded in Eusebius 3.39)
“So then Matthew wrote the oracles in the Hebrew language, and every one interpreted them as he was able.”
4. The earliest manuscript bearing the title "according to Matthew" is very likely P64/67 (these fragments are usually considered part of the same original manuscript).
5. Patristic citation -
The earliest statement that is 100% unambiguous on this matter comes from Irenaeus of Lyons, writing approx. AD 180. He attributes the Gospel of Matthew to Matthew, quotes repeatedly from the document, (see Irenaeus Against Heresies 3.1.1)
6. Origen said the first gospel was written by Matthew in Hebrew. (HE 6.25.4) Eusebius of Caesarea, History Ecclesiastica.
7/ Eusebius — Matthew had first preached to Hebrews and wrote in their own language (HE 3.24.6)
There are internal evidences that also support but it is by viewpoints.