Anyways, I didn't mean to ramble on, I'm just really tuned into this stuff, and I have nothing to do with the space program, but I'm an interested observer.
So, Artemis II will launch soon, and it will not even orbit the moon. It will go on a free-return trajectory like Apollo 13 (after the incident). It will still be stunningly cool, and there are 4 people aboard instead of the Apollo era 3 crew. I'm sure there will be a lot of attention, and for good measure.
The average person is probably expecting us to make a real moon landing soon, but it's probably a few years away. The reason is because it took so long to develop SLS/Orion and so much money that there was not much money left over for the lander (HLS). By the time they got around to awarding the lander, there were several contendors. Old Space (Lockheed/Boeing and some others), Blue Origin (Jeff Bezos' company), a couple more, and Space X. Space X was already developing Star Ship/SH, and they won the bid. They were the furthest along, and they already had billions of their own money invested.
Now, I'm sure you've seen the videos of SS/SH crashing, blowing up, and in general not doing too well. It needs to be stated here that Elon Musk is simply not scared to push the envelope and fail. These rockets they are sending up are purely iterations of each other, and they are being thrown together in a way that a production rocket never would. But they are making progress, including landing the SH part of SS onto the tower.
The hard part is and always will be re-using the upper stage, which in this case is the StarShip portion of the rocket. They've been evolving the design for years, experimenting with tiles, different fin combinations, different engine strategies (hot staging!). They're actually pretty close to being able to bring SS back, intact, and landing in back onto the launch tower. They've had several controlled re-entry tests, and they're getting the heat shield dialed in. The upper stage is so much harder to save, because it's going so much faster and takes so much more thermal abuse.
Again, it's not well known or publicized by the press, but one "flaw" in the SS/SH concept is that once SS reaches space, it almost immediately will need to be refueled. It's essentially empty. You remember the giant external tank on the space shuttle? We threw that away after every launch. The main engines on the space shuttle were paperweights after tank separation. The only fuel it had was it's little orbital maneuvering thrusters (OMS).
Well, guess what....orbital refueling has never been done. At least, nothing beyond small experiments. What Space X plans is to land the SH rocket, refuel, mate it up and fly a new version of SS up called tanker. They haven't really released very many details about this portion of the plan, but essentially I think there will be no humans, no cargo (other than fuel). It's only job is to get a tank load of fuel into space, refuel the other SS, and come back. And in order to do this enough to send SS to the moon or anywhere else, it needs to do it maybe a dozen or more times. I've seen reports that it will take up to 16 tankers to fully fuel up starship.
So as you can imagine, complex.