No, there is no rule of thumb.
It really depends on how dependable and maintainable you want your code base to be. If your project is a small class or one-shot utility, you may not need any unit tests at all. If, on the other hand, it is a framework or core program that will be used by many people, you may need extensive unit tests, and you'll probably need them from the beginning.
Unit testing, when used correctly, guides your overall software design. Testable code is easier to maintain, easier to reason about, and has fewer bugs. This is as true from day one as it is at the end of your project. Delaying this process is based on the false idea that unit testing takes more time than just writing an application and testing it manually. While unit testing takes a little longer to set up, it pays for itself the first time you have to re-run the tests.
Unless you are writing in a dynamic language with a REPL, I honestly don't see how delaying your unit tests is going to help you. I use unit tests as a shim for trying out experimental code. When I have code that works, I graduate both the unit test and the working code to "first-class" status in my project, and the unit test serves as a design prototype for the actual code, as well as verifying that the code still works after a refactor.
If you are working in a dynamic language with a REPL (as opposed to a statically-typed language like C#), unit tests become even more important, because you no longer have the safety net of static type verification during compilation.
Nowhere is this philosophy more evident than in the SQLite code base. SQLite has roughly 84 thousand lines of production code, covered by more than 90 million lines of test code. I'm pretty sure the author wasn't ever thinking "so when should I start writing unit tests for this thing?"