It's escape velocity, not escape speed - and it's orbital velocity that matters here, we're not escaping entirely. If you're in the same place, travelling at the same speed, but pointed down, you're not in orbit, right? It's the same if you're pointed straight up. You need to be at an orbital altitude and travelling at the right speed
in the right direction.
(well, any combination of speed, direction, and position will be an 'orbit' in some sense, in that there's a conic section you're on that you would follow if you were in freefall. But if you're sitting still over a planet then it's the degenerate ellipse that's a straight line down to the planet's core).
So in the absence of atmosphere the ideal ascent trajectory would look pretty much like a Hohmann transfer orbit: you'd accelerate horizontally until you were in orbit at surface level, and then you'd do the minimum energy transfer from that orbit to a higher orbit. In reality it's worth getting to altitude where the air is thinner before turning horizontal, but even so, the vast majority of a rocket's acceleration is horizontal, not vertical.
You can do the maths, but if you want to really understand these things, play Kerbal Space Program. Seriously.