You'd think so, but nope! Going straight up will get you to space, but you'd fall right back down the moment you cut off your engines. The way to get into "orbit" (which is how you stay in space and experience zero G without burning fuel) is by moving sideways fast enough that your sideways motion creates a ballistic arc that keeps your altitude above Earth. They're still in freefall, but moving so fast they "miss" the planet. From orbit, they can then burn the engines at the right time to break out of orbit and fall towards the moon once they get close enough, with precise heading that allows them to "miss" it and fall back down to the planet in what's known as a free return trajectory. That's how this works in a nutshell, but orbital mechanics are tough to wrap your head around so I'd strongly suggest spending some more time reading about it!