Your conflation of TDD with automated testing is not helpful.

As software developers, the essence of our profession is to automate repetitive tasks. If you have a rigorous manual testing methodology for your software, it should be a trivial task to turn that test specification into automated tests. The absence of a suite of automated tests is a major red flag in any non-trivial software project - it strongly suggests that either the developers do not care about quality, that they do not understand their work well enough to manage quality in a systematic way, or that they are too haphazard and disorganised to manage their project appropriately.