Could Europeans have invented the wheel independently of outside source?

Yes. It's even possible that the wheel was first invented in Europe. The three most plausible places for the invention of the wheel are the western steppe (Ukraine, which is considered part of Europe today), the Balkans, and Mesopotamia. The first two are much more likely than Mesopotamia.

Whether the wheel was invented independently in the western steppe and the Balkans is unknown. It's possible. Notably, the main uses for the wheel in the two areas were quite different (ox-drawn wagons - perhaps the first mobile homes - and mine carts).

For more detail on this, see https://www.reddit.com/r/AskHistorians/comments/ayuy1c/is_there_any_way_of_knowing_which_civilisation/

The chariot (a fast light two-wheeled cart with spoked wheels) was probably developed in Central Asia (the oldest examples are from the Androvono culture, Kazakhstan and nearby), and spread east, west, and south from there. How much of the spread was due to the idea of the chariot spreading, or due to chariots going east, west, and south, or chariots and their drivers and riders going east, west, and south is unclear. All contributed, but the uncertainty is how much and when each of these methods of spread contributed.