The facts on the ground are that this particular workspace is doing well enough to write checks that do not bounce without a version control system.
Changing workflows and training employees comes with capital costs and business risks. Not using a version control is not a moral failing. It is a business decision. My advice is to understand why it is a business decision and what went into making it and not assume that immediately implementing version control is a local optimization let alone a global optimization for the business.
To put it another way, if the need for version control at this particular time in this particular context was obvious, there would be no need to ask the internet for arguments. The important argument would be to point to actual problems easily solved by version control that seriously and actually effect the business. Keep in mind that lots and lots of software has been and still is produced without version control.
None of which means I don't like version control and don't use it for my own projects and would not recommend it if someone asked my opinion (and probably would recommend it even if they did not since that's just my idiom). What it does mean is that walking into an ongoing business as a new employee and telling everyone that they don't know what the fk they're doing encourages people to take sides. Looking to win the argument over version control means looking to make other people lose the argument and that means people will disagree just on the basis of winning and losing.
Anyway, my random advice from the internet is to start using version control in ways that help you do your job without requiring anyone else to use it or deal with it. If people see it makes your life easier and does not impose on them at all, they'll naturally be curious if it will make their own life easier.
It will take time and might not work at all. At the very least you won't be telling you're teammates that they're wrong and save all the time that would be spent arguing. At best, you'll show them the advantages version control since might solve of the problems that version control can solve...but again, use version control in a way that does not create problems for anyone else and that means significant, effort and discipline and empathy on your part. All of which is harder than making arguments.
Good luck.