Well, first and foremost... if your manager says that you can't use git, it just means that you can't use their git. If you use your own git with a private project, you can get your work done and not worry about it.
However, I'm a bit concerned because this seems like your company has bad practices in general:
- No git! Clearly, this is a huge no-no for software development.
- No code reviews. If you're a JR, it seems like the best place to learn.
- No testing. Nobody expects you to test your work, so they must expect you to write perfect code without a single issue!
- No project management framework (Jira, Trello, or anything of the sort). The fact that you setup your own board is great.
- Nobody in your company seems to have an idea of how to build software.
It appears that you're working for a consulting/outsourcing company. You were sold as a much more experienced developer than you actually are.
Honestly, my advice would be to find a different job. It's definitely not easy, but it may be your best chance to get into an environment where you can grow as a developer and not get infected with terrible "development" practices or lack thereof.