The Karman Line is one of the most commonly-used definitions of the "edge of space". As an airplane flies higher in the atmosphere, the air gets thinner and thus the lift decreases. This can be compensated by flying at a faster speed. The Karman line is the altitude at which you would need as much speed as the orbital velocity. You are no longer flying; you are in orbit.
Earth has a gaseous atmosphere, and a Karman line that calculates to about 100 km.
This Space.SE question examines the Karman line of a planet without an atmosphere (i.e. a solid surface). The general consensus of the answers is that the solid surface itself is the "edge of space". The moon is such a body.
So we have...
- the edge of space with a solid surface (moon).
- the edge of space with a gaseous atmosphere (Earth).
What about a planet (or moon) with a liquid surface -- namely, could there be any contrived, theoretical scenario where the Karman line occurs below sea level?
The oceans do not necessarily have to be water (e.g. ammonia, mercury, or hydrocarbons are fine). You may adjust temperature, pressure, and gravity to any plausible values that support liquid oceans. Presumably, to keep the oceans from boiling away, there would need to be a solid crust above the ocean, or some atmosphere inadequate for flight (your choice).
Interestingly, such a possibility would mean that no creature or vehicle could "swim" to the surface of their ocean.
Obviously, Earth itself proves you can have a Karman line above a liquid sea level.