Short answer
– The plainest evangelical answer is: the author is not named in the text (Psalm 1 has no superscription), so the exact human author is unknown.
– Two common evangelical approaches: (1) the traditional view that many Psalms ultimately reflect Davidic tradition and that David is often associated with the Psalter, and (2) the scholarly-evangelical view that Psalm 1 is best read as an anonymous “wisdom” or editorial introduction to the whole Psalter written by a wise Israelite or an editor, not necessarily David himself.

Why evangelicals take those positions
– Textual fact: Psalm 1 lacks a title (“A Psalm of David…”) that appears on many other psalms, so there is no internal credit to David or anyone else. That leads many careful readers to call the author “anonymous.”
– Literary function: Psalm 1 reads like a wisdom poem (compare Proverbs) and functions as an introduction to the whole book of Psalms—contrasting the way of the righteous and the wicked and stressing delight in God’s law—so many conservative scholars see it as composed by a wisdom teacher or by an editor who placed it at the start of the Psalter.
– Tradition: Historically Jews and Christians have strongly associated the Psalter with David (he is the dominant figure and a model psalmist), and many evangelicals continue to honor Davidic connections where they appear. Some therefore read Psalm 1 in the light of Davidic worship tradition even if the poem itself is anonymous.

Evidence cited by evangelicals
– For anonymity/introductory-wisdom view: absence of a superscription; the Psalm’s thematic and stylistic similarity to wisdom literature (e.g., “blessed,” “meditate,” contrast of righteous and wicked); its placement at the head of the Psalter.
– For Davidic association: ancient Jewish and Christian tradition that links many psalms to David and the general view that David’s role as worship leader shaped Israel’s psalmody.

Practical/theological significance (why authorship matters little to most evangelicals)
– Whether David wrote it or an anonymous Israelite, evangelicals emphasize the Psalm’s message: true blessing comes from walking according to God’s way and delighting in his law, meditating on it day and night (Ps 1:1–2). The authority of the passage rests on Scripture, not on the particular human author.
– Application: Psalm 1 is often used in evangelical teaching to encourage Scripture meditation, holiness of life, and the contrast between the godly and the ungodly.

If you want, I can:
– Quote Psalm 1:1–2 and unpack the words phrase-by-phrase from an evangelical devotional perspective, or
– Summarize how several evangelical commentators treat the question of authorship and dating. Which would you prefer?