Short answer
– From a typical evangelical Christian perspective, the most likely human author of Deuteronomy 7:9 is Moses (with the recognition that the Pentateuch may have received later, God‑directed editorial shaping).

Why evangelicals usually say Moses wrote it
– Deuteronomy is presented in the book itself as the farewell speeches of Moses to Israel (Moses is the speaker throughout).
– Jewish and early Christian testimony uniformly attribute the Torah (the first five books) to Moses. Jesus and New Testament writers treat the Pentateuch as “Moses” (for example, they cite “Moses said…” or call it the Law of Moses). Evangelicals take those testimonies seriously as part of the Bible’s own witness.
– Evangelical theology of inspiration holds Scripture as God’s word written through human authors. So even where redaction or later editorial work is acknowledged, Moses is regarded as the primary human author or source through whom God conveyed these words.

How evangelicals handle critical scholarship
– Many evangelicals accept that there may be later editorial work or additions (for example, phrases that reflect later perspective), but they still affirm Moses as the principal author and the book as fully inspired.
– Some conservative evangelical scholars argue for strong Mosaic authorship and unity of Deuteronomy; others allow for a Mosaic core with subsequent faithful editing. Either position maintains that the text is authoritative and divinely guided.

Practical theological note (why it matters to evangelicals)
– Attributing Deuteronomy to Moses supports the continuity and authority of the Law in God’s covenant dealings with Israel. Deut. 7:9 is read as part of Moses’ instruction about God’s faithful covenant‑keeping and the obligations of God’s people—truths evangelicals see as consistent with the whole Bible and ultimately fulfilled in Christ.

Further reading (evangelical-friendly)
– Peter C. Craigie, The Book of Deuteronomy (NICOT) — a conservative commentary.
– John H. Sailhamer, The Meaning of the Pentateuch — argues for a Mosaic core and theological unity.
– Short evangelical introductions to the Pentateuch or to Old Testament theology for broader context.

If you want, I can summarize arguments for Mosaic authorship in more detail, point to specific New Testament passages that assume Mosaic authorship, or suggest a short reading list focused on Deuteronomy.