Depends, what's the reasoning? Because technically anyone can start a project even without Git. Or even without a computer. Someone can use a pen to write code on a paper.
Depends on what you mean by "a project". If it's policy related, maybe it's company's policy that all code that is written must be stored in a certain way for multitude of reasons.
They don't have a reason. There's no policy that keeps them from doing this. Sure, the whole point is to ultimately have the code in a common place where backups and code review can happen, but if it's a matter of starting something sooner because it takes a few days for the request to flow through to get things set up, they are not constrained by that AT ALL. They can create a git repo with git init immediately, start working, and once the repo is set up in the common area, git push all their work into it. Rather than train people on this, we spend time trying to hasten the common area repo setup time and put additional unneeded burden on the team responsible for that.
It doesn't matter. They are centralized on servers that are ssh accessible, creating it is effectively mkdir and git init.
It's not about how long the action takes, it's about how much the team responsible for that is loaded and can prioritize things. Every team needs more round tuits. Anyone who works in an IT support role knows this. The point is that they can self-service immediately and there is no actual dependency to start writing code and using revision control, but people will trot out any excuse.
But why can't the teams themselves do it? All places I've seen or been to have had teams able to create their own repositories, either they use cloud Git providers like Bitbucket, Gitlab or Github, or they have self hosted Gitlab, Github etc.
Lots of places (unfortunately) restrict repo creation, or CI pipeline creation. The platform team might need to spin up the standard stack for your project, VON access added for AWS environments etc etc. In the sorts of orgs where this happens doing it properly is more important than getting started.
Tons of people never even touch git cli, they use some gui frontend/IDE.
Tons of people who DO use git cli don't know git init. Their whole life was create a project on github and clone it. Anyway initting new project isn't the most "basic" thing with git, it is used less than .01% of total git commands
if you combine the above easily MOST people have no idea about git init
Depends on what you mean by "a project". If it's policy related, maybe it's company's policy that all code that is written must be stored in a certain way for multitude of reasons.