Assuming you are a developer, start writing some.

Next bug you find that needs a unit/functional test (e.g. it is caused by a simple error in transformation in one function), write the test first as a table of inputs vs outputs, find it fails, fix the function, and leave the test in. Gradually, the code base will contain unit tests which are useful, people will see they are useful, and other people might start using them too where appropriate.

You are unlikely to persuade them without actually doing what you say is beneficial and exposing others to its benefits.