Again, where are members of Starfleet called "astronauts" by Starfleet? Starfleet personnel are trained to work on Starfleet ships and facilities. That probably includes emergency procedures, like finding a escape pod. Maybe some weapons training and basic first aid.
Military Academies are all four programs.
Are post grad degrees in dispute here? Why bring them up?
The term "astronaut" comes from the Greek words for "star sailor" and was once reserved for military-trained professionals. The issue isn't that Roddenberry said they were astronauts, patently they are. The issue is that he considered that the crew consisted of 'trained' astronauts.
I only brought up the post-grads to cover off Starfleet training that takes longer than 4 years but I have taken a look at Memory Alpha if that helps, which does cite sources for the standard assumptions:
"The Academy program typically lasted four years, though certain programs lasted five, six, or eight years. (
TNG: "
The First Duty", "
Conundrum";
TOS: "
Bread and Circuses")"
"The Academy had a separate program for the training of
enlisted crewpeople, which included receiving basic training and attending the
Starfleet Technical Services Academy on
Mars. (
TNG: "
The Drumhead", "
Eye of the Beholder";
LD: "
Reflections")"
"Post-graduate options
So, you can make assumptions on what kind of 'basic training' enlisted crew undergoes but following naval traditions, it could be the space equivalent of the following:
"Recruits are instructed on
military drill,
watchstanding,
basic seamanship, water survival skills,
first aid, basic shipboard
damage control,
firefighting, shipboard communication, familiarization with the
M9 pistol and
Mossberg 500 shotgun, pass the confidence chamber (
tear-gas-filled chamber),
PT, and the basic essentials on Navy life. Recruits also attend many classes throughout boot camp on subjects such as Equal Opportunity, Sexual Assault Victim Intervention,
Uniform Code of Military Justice, recognition of naval aircraft and vessels,
U.S. naval history, and more. In order for recruits to pass boot camp, they are physically and mentally tested on a 12-hour exercise called
Battle Stations which consists of 12 different scenarios involving firefighting, navigating smoke filled compartments, first-aid knowledge, survival at sea, mass casualties, shipboard flood control, bomb detection, and many other skills that they have been learning in the previous 7 weeks."
Enlisted personnel specialise on the job and get promoted based on experience. So Rand, who is a petty officer first class, would have all the above training plus her years of experience in whatever she was doing up until now, plus her skills as Kirk's yeoman. Mears is younger, possibly more junior, but her basic training would cover the same stuff, which very likely would include basic operation of Starfleet vehicles.
One could argue that basic training would not automatically cover helm or navigation (traditionally officer territory) but not exclusively since both Rand and O'Brien (albeit experienced petty officers) also appear to be trained.
At any rate, I stand by my initial point that Spock was not 'essential' to fly the shuttle.
I suppose another way to frame it is to ask whether they have ever featured any Starfleet character in any discipline, of any rank, who was stated to have been unable to pilot a shuttle?