Could an 1800-era state build the Kiel Canal?

Could a Kiel Canal have been built with the technology available around 1800?

Theoretically yes, but it would have required a very large workforce.

The period's technology could in principle produce a Kiel Canal. The limiting requirement in the brief answer is an enormous workforce rather than a missing technical concept. Nothing in the exchange establishes that the project would have been quick, cheap, or politically practical. The answer concerns narrow technical feasibility rather than a detailed engineering estimate.