Some fun trivia—the planet Kerbin from Kerbal Space Program is the opposite case. It has a radius of 600km, versus Earth's 6378km, but is exactly 1 Earth g on the surface. This implies it's over 10x as dense.
I.e. air-breathing aircraft + chemical rockets would work, as would other exotic solutions
Another way of looking at it—on a body with no atmosphere, the most efficient way to attain orbit is to be on the equator, point your spacecraft "east" (prograde to rotation), and elevate the nose just enough to avoid lithobraking on that mountain in the distance. If Earth were such a beast it would take roughly 7000 m/s delta-V to do this. IRL, because you need to get over the atmosphere first, it takes about 9000; the "gravity turn" is a compromise between losing energy to gravity/steering versus losing it to drag. So any exotic system—air launching a Saturn V is definitely exotic!—would help with efficiency, but I don't see that it would radically alter the situation.
