You don't need to sustain thrust the entire time you just need to reach a significant portion of escape velocity energy early in your launch (which is what most launches need anyways just this time you need slightly more energy than the efficient way). This is not something we have trouble doing, for reference we launched New Horizons directly into above escape velocity speed with an Atlas V rocket. The only reason we haven't done that kind of launch to the moon in real life is it's far cheaper and more efficient to do that "normally" not because we couldn't.
