Well, with a single launch site you will need to wait for an orbit with a multiple-launch architecture yes.
But if you have multiple launch sites like SpaceX does, one in Texas, and the other in Florida, you can possibly make it in the same orbit. It requires precise timing but it would be possible. You launch the Falcon Heavy rocket first with the equipment, then you launch a regular Falcon rocket with the crew, you dock them on-orbit then do the mission. Then that would do an Apollo profile landing mission.
A single Falcon Heavy can also launch a crewed capsule on a manned lunar flyby just by itself. I mean even Proton can do it and it has less launch capability. Also, making a bugbear out of Earth docking is silly. I mean the Chinese expect to build an Earth orbit space station right? If docking is that unreliable you couldn't even have a space station to begin with.
If you need a large delivered payload to the Moon proper you can either refuel the payload in orbit to increase delivered mass, or you use automated missions to deliver the larger payloads *ahead* of the human mission, or both. Without humans you can use all sorts of slow-moving but highly efficient propulsion systems to deliver the requisite payload instead. You could use solar-thermal or solar-electric propulsion for example. Solar-thermal with LH2 has like twice the ISP of a LOX/LH2 stage and is kind of simple to implement. It works more or less like a solar water heater but you heat LH2 and vent it out. You have increased ISP with those methods because part of the propulsion momentum comes from solar power and doesn't need to be carried as mass.
Unfortunately the past NASA leadership lacked a clear vision to implement a lot of these ideas. But right now, I think, if SLS gets cancelled eventually which is highly likely, then NASA will have the huge funds to design all sorts of Moon/Mars architectures different than the one outlined in the Vision for Space Exploration (VSE) made by Mike Griffin back when George W. Bush was President. They are already funding a lot of projects under the NASA Gateway project which is a manned space station orbiting the Moon.
If you read the NASA plans for lunar exploration back from when Goldin was President of NASA you will see they had a much different idea of how to do a launch architecture compared to that of Mike Griffin's time. Mike Griffin designed an architecture which assumed no new technology had to be developed at all, even if the technology to be developed was trivial, so NASA ended up with a design which uses the SSME as an expendable main engine for example. Which is just silly.
The Chinese CZ-9 at least uses expendable main engines. But it is still a huge rocket which will likely require new larger construction buildings to make the sections of the rocket (NASA at least had the Michoud facility in Louisiana which built the Saturn V/Shuttle), together with the cranes to move them, the machines to weld them, larger barges to carry them to the launch site, new launch site, new test stands, etc. For a rocket you will likely launch one every two years and which disentegrates into launch. Hugely expensive.
