Short answer: From a typical evangelical Christian perspective, the most likely author of Matthew 7:7–8 is the Apostle Matthew (also called Levi), the tax collector who became one of Jesus’ twelve disciples and is traditionally credited with writing the Gospel that bears his name.

Key points an evangelical would emphasize

– Identity: Matthew/Levi — a Jewish tax collector called by Jesus (see Matthew 9:9; parallels in Mark and Luke). Tradition identifies him as the author of the Gospel of Matthew.
– Early church testimony: Second‑ and third‑century sources (notably Papias as reported by Eusebius, and later writers such as Irenaeus, Origen and Eusebius) attribute the Gospel to Matthew. Papias says something like “Matthew compiled the sayings in the Hebrew language,” a testimony evangelicals commonly cite, though its precise meaning is debated.
– Apostolic eyewitness status: Evangelicals highlight that Matthew was one of the Twelve and therefore an eyewitness of Jesus’ ministry. That apostolic connection undergirds the Gospel’s authority in evangelical theology.
– Date and audience (typical evangelical view): Many evangelicals date Matthew’s Gospel in the late 50s–80s AD and see it written primarily for a Jewish‑Christian audience (hence strong Jewish themes: fulfillment citations, Old Testament quotations, “kingdom of heaven” language).
– Literary and theological marks that fit Matthew: The Gospel emphasizes Jesus as the fulfillment of Hebrew Scripture, includes structured teaching (five major discourses, including the Sermon on the Mount where 7:7–8 occurs), and presents material likely preserved from an eyewitness or eyewitness sources. Those features are taken as consistent with Matthean authorship.
– Modern evangelical scholarship: While evangelicals accept the traditional attribution to Matthew, many also engage critical literary questions (e.g., Markan priority, Q material). A common evangelical position is that Matthew the Apostle authored or at least compiled the Gospel we have, perhaps using earlier sources (including Mark and teaching collections) while preserving authentic apostolic witness.

How this relates to Matthew 7:7–8
– Matthew 7:7–8 is part of the Sermon on the Mount (Matthew 5–7), a major teaching block. From an evangelical standpoint, the passage is an authentic record of Jesus’ teaching preserved by an apostolic witness (Matthew), and it therefore carries authoritative weight for doctrine and practice (especially teaching on prayer and God’s gracious response).

Caveat
– There is scholarly debate (even among evangelicals) about details: whether Matthew wrote originally in Hebrew/Aramaic (as Papias might suggest) or in Greek, exactly when and where it was composed, and how Matthew used other sources. But the consensus in evangelical tradition remains that Matthew the Apostle is the most likely author.