Short answer
– From a standard evangelical perspective, the most likely author of Isaiah 43:16, 18–19 is the prophet Isaiah (Isaiah son of Amoz), the eighth‑century BC prophet who ministered in Judah during the reigns of Uzziah, Jotham, Ahaz and Hezekiah.

Who Isaiah was (evangelical summary)
– Isaiah son of Amoz is introduced in Isaiah 1:1. He was a Jerusalem prophet called by God (Isaiah 6), active in the 700s BC, and is traditionally understood to have been an adviser to the kings of Judah.
– Biblical details associated with him include his calling vision (Isaiah 6), a wife described as a “prophetess,” and children whose names were prophetic signs (e.g., Shear‑jashub, Maher‑shalal‑hash‑baz).
– Early Jewish and Christian tradition attribute the whole book to Isaiah; some early traditions also say he suffered martyrdom (tradition records he was sawn in two, cf. Hebrews 11:37’s general reference to prophets’ sufferings).

Why evangelicals accept Isaiah as the author of these verses
– The book itself repeatedly names Isaiah as the prophet (e.g., Isaiah 1:1, 6:1), which evangelical scholars take at face value.
– Evangelicals appeal to the unity of theological themes and consistent prophetic voice across the book as evidence of a single prophetic author.
– The Great Isaiah Scroll among the Dead Sea Scrolls (ca. 2nd century BC) preserves the book as a single work and is used by evangelicals to argue for the long attestation of Isaiah’s text and message.
– Many evangelicals also accept predictive prophecy: passages in Isaiah that speak of events later than the eighth century (e.g., the “new exodus,” Cyrus, the suffering servant) are understood as genuine foretelling by Isaiah rather than later additions.

Historical and literary context of Isaiah 43:16, 18–19
– Isaiah 43 falls in a section filled with messages of comfort and redemption. The chapter contrasts the LORD’s unique power and saving acts with idols and foreign nations.
– Isaiah 43:16 recalls God’s decisive action in the original Exodus (“making a way in the sea”), using that deliverance as a pattern and guarantee for future salvation.
– Isaiah 43:18–19 turns from the past exodus to promise a “new thing” — God will do a fresh act of salvation (often called a “new exodus”), making a way even in the wilderness. Evangelicals typically see this promise as having immediate relevance to Israel’s restoration and deeper fulfillment in the work of Christ and the new covenant.

Theological significance (evangelical emphasis)
– Divine sovereignty and redemption: the verses emphasize Yahweh as the one who acts to save, able to do the impossible (parting seas, making paths).
– God’s faithfulness and renewal: God brings new mercies and unexpected deliverance; believers are urged not to be bound by former patterns but to trust God’s present work.
– Typology and fulfillment: Isaiah’s “new thing” is often read typologically — first pointing to restoration after exile, ultimately fulfilled in Christ and the inaugurated new creation (cf. NT uses of Isaiah’s themes in the Gospels and Paul).

Practical and devotional notes
– Evangelicals often use these verses to encourage trust in God’s ability to intervene and to expect God to do fresh things even in hopeless situations.
– The passage is cited in preaching and worship to stress God’s power to transform circumstances and to call people to faith rather than nostalgia for past blessings.

If you’d like
– I can give a short comparison of how critical (academic) scholarship treats Isaiah’s authorship versus the evangelical view, or
– I can walk through Isaiah 43:16, 18–19 verse‑by‑verse from an evangelical devotional or expositional perspective. Which would you prefer?