Maybe a dumb question, but why do you need to launch directly to the moon instead of launching to earth orbit then doing a transfer? How much better is the direct method delta v?
I don't know if one trajectory is more efficient than the other, but space propulsion systems are quite tricky and if I remember correctly the X prize was trying to incentivize doing things on a budget to "democratize" access to the moon. It was basically the cubesat of moon rovers. If you think of technical decisions through that lens, it therefore makes sense to ask your launch provider to do as much of the work as possible since they already have a second stage capable of getting you there, instead of designing a bigger payload with a more capable propulsion.
Yeah, Moon flight trajectories could be somewhat head-scratching.
Imagine the Moon orbit is in the plane of the Earth equator (it's not) and you're launching your rocket also to the equatorial plane. Moon rotates around the Earth in one month, LEO period is about an hour and a half, so every approximately 1.5 hours you're passing via point in orbit which has the necessary phase (angular) distance relative to the Moon. If you, for example, going via a Hohmann orbit - half-ellipse from LEO to Moon orbit - you just start translunar injection burn at the point of LEO (approximately) opposing to the Moon. Life is good, you don't need to think much and plan ahead - just gas 'n go.
Now, real world. Moon orbit is 5.1 degrees from ecliptic plane (the plane of the Earth orbit around the Sun), and Earth axis is 23.44 degrees from ecliptic, and there are no convenient spaceports on equator - Alcantara still doesn't launch, and Sea Launch is out of business. So the plane of your LEO orbit is likely different from the plane of the Moon orbit. What does it mean? Two different planes intersect in just one straight line - which in this case passes through the Earth center (or somewhat close to it). If you'd start your engines near the intersection point - when your position on LEO will be near that intersecting line of LEO plane and Moon orbit plane - then you'll raise your apogee and it will hopefully bring you to the vicinity of the Moon orbit. Now, the question: will Moon be there, near that point of its orbit? If you carefully waited on LEO - or launched to LEO in the proper time, taking all this into account - then it might. If not - well, your spacecraft will fly to the Moon orbit and back, as did some Zonds launched in USSR. So here we clearly see the need for the correct launch window.
(And if you won't start your engines close to that intersection point - then you might get as far as the radius of the Moon orbit, but will be away from the orbit itself - the Moon orbit is just a circle, and you'll fly towards some point of the sphere with the radius of the Moon orbit. Could be completely different areas of space, so you need to take the plane of the Moon orbit into account)
Theoretically we might try to change the orbital plane. It's either very expensive in terms of delta-V - you usually don't have nearly the amount of fuel needed - or takes some less fuel and a lot of time - as you need to travel far away, to make the plane change cheaper in the region where the orbital velocity is much smaller.
Realistically it's better to launch towards correct plane and in correct time, and plan ahead. Funny, the Earth-Moon system seems rather simple, and yet we still need to be smart enough to navigate here.