How far back can plausible Atlantic crossings be traced?

What is the earliest plausible transatlantic voyage?

Viking crossings are certain, while Roman or Celtic possibilities remain difficult to separate from maps, oral tradition, and later mythmaking.

The answer treats Viking voyages as the secure baseline and earlier crossings as possibilities rather than established events. Roman maps and Celtic traditions may preserve clues, but oral histories can accumulate embellishment as storytellers transmit them. Maritime plausibility alone does not establish that a voyage occurred.