I'm not a pilot, but I've already spent some time writing a flying scene by running the whole sequence in a flight simulator.
Some things to think about...
There are videos on YouTube of inexperienced pilots flying complicated planes in the simulator. People are interesting. There have been a number of cases where a pilot, in a stressful situation, was able to pull off something that was nearly impossible when they gave a bunch of un-stressed pilots of similar levels of training the problem in a simulator. There are also cases where pilots have gotten stressed out and flown a perfectly functioning aircraft into the ground.
A G650ER is not single-pilot rated. This means that your hero is going to have a very hard time taking off safely without a second person, for the want of extra hands. I don't know offhand if the G650ER has a tiller control or not, but picture trying to steer the nose-wheel of the airplane while also steering the control surfaces.
The G650ER is also the sort of plane you need to get specifically certified for.
There's going to be checklists and a quick reference guide in the aircraft, but your hero isn't going to know where the buttons are quickly. Nor will they necessarily be able to quickly figure out how to set up the weights-and-balances calculator to know what speed to pull back on the nose, etc. Some time to familiarize themselves would help.
There's enough standardized that your hero can find the throttle, the steering controls, etc. Most engines just have a "start" button these days because it reduces pilot workload and damaged engines. There's a little arrow thingie in the corner of the display to represent stall speed. Okay, certain death from the antagonist versus potential death from a screwup makes this an easy call.
If I remember correctly, the G650 has a gust lock on the flight controls, to keep the plane from moving around in bad weather, and you need to know to retract that before you try to turn on the engines or something like that. So having them at least read the takeoff checklist (you might be able to even find it on google) would be important.
But, especially at landing, things are going to be dicey. I tend to break abstract skills down into two large chunks. Some stuff, like painting or drawing, you can do at a fast or slow pace. Other stuff, like pottery or glassblowing or flying aircraft, you have to do everything exactly right at full speed, or you are going to be in trouble. Part of what they do with flight training is get you to the point where you are able to do the right thing without thinking about it on a simple aircraft and then ratchet up the complexity. The airplane already lands at the slowest safe speed. If there was a slower safe speed, they'd land at that speed instead. And your pilot's brain is going to be full. They are going to PIO (Pilot-Induced Oscillation) the airplane. They are going to know that they are PIO-ing the plane rationally but can't quite get it to stop. They are going to have to figure out how bad they want to land, or if they can make a bunch of tries, getting closer to landing each time.
Oh and a single-engined piston plane has very little throttle lag, but a jet is going to take a second or two to spool up or down when you adjust the throttle.
I guess it depends on how heroic you want your fiction to be. It could be the point at which some chunk of your audience can't accept where the story is going. Or it could be your hero avoiding a battle and instead battling themselves.
And you'd really not want things getting complicated. They are going to need plenty of extra runway, because it's pretty much a guarantee that they are going to nurse the aircraft up instead of risking damage. The weather needs to be favorable. They probably don't want to go very far, or even do things like retract the landing gear.
And also remember that a *lot* of bad landings where the aircraft is ruined are still survivable. The penalty for a hard landing is broken landing gear, but a lot of pilots do that and walk away.
Or you could always have your hero know another pilot who let them sit in the right-seat or a more sophisticated aircraft while they flew, so they at least have some basis for understanding. If the aircraft is single-pilot-operation, a non-pilot or a pilot not qualified in that particular aircraft can sit in the right seat and still help out if no other regulations (like transporting paying passengers) still require two pilots.