TDD isn't "THE" way, but test coverage helps. It's not fun (at least not for me), but it's less aggravating than breaking something 6 months down the road in some non-obvious way. I'm human, so I assume I'll screw something up eventually. Having test coverage helps keep me from shooting myself in the foot later.
You should often be able to at least create an automated acceptance test for what you're doing (e.g., "as a user I want to click this button and see XYZ"). This is usually extremely decoupled from the implementation so it should survive refactoring. So then do your exploratory code, get the test passing, and then refactor, introducing lower-level tests.
If that doesn't seem doable you might be taking on a task that doesn't have a good set of requirements. Writing code without any concrete use case in mind is fun and all but that kind of code should usually be limited to a prototyping sandbox.
Consider (for instance) a program to translate ABC music format to proper sheet music. It's easy to say the basic requirement: "The program has to accurately translate ABC format to legible and easy to read sheet music." But even a start at automating a test for that would require converting a graphical representation of sheet music back to the basic notes, and that problem is at least an order of magnitude harder than writing the original program, without factoring in the "easy to read" bit at all. (PS This is a real issue for me, if someone knows of a decent open source sheet music to MIDI/ABC convertor I'd love to hear about it.)
A unit test for a piece of code like this might be "Given that the time signature for the music is 3:4, the software puts 3:4 in the appropriate place on each line of output".
You then might write a variety of cases testing that it deals correctly with (say) a changing time signature at some point in the piece.
The upside of this is when you try and fix another bug which has a knock on effect on this bit of code, lots of your tests are going to fail- immediately identifying where the problem is (or at least letting you know there is one!)
But okay, is it really so much easier to write a test which just tests changing the time signature? It's still going to require doing OCR. And if I'm really testing it, I've got to make sure the time signature change comes at the correct point, which requires OCR on the notes around it. Also the bar lines (to makes sure the time signature change is reflected in the notes per bar and not just by writing a new time signature out and otherwise ignoring it).
Now, it's perfectly reasonable to have unit tests that the code correctly recognizes time signature changes in ABC format. (And it looks like I forgot to write them: I see inline key changes in the tests but not inline time signature changes.) But that's only testing half of the problem; and it's the easier half by far.
Don't you still have the same problem colomon described here, though? Testing your stated condition "the software puts 3:4 in the appropriate place on each line of output" still implies some form of image recognition on the graphical output.
Prototype all you want without tests, but once you've settled on a design & are ready to make it production-ready you should spend time at least writing unit tests for your work or (ideally) take what you've learned & re-apply to a clean design written in a test-first manner.
You might think this is a waste of time, but putting code into production without tests is going to give you more trouble in the long run.
It doesn't slow me down, and I can be sure that my feature is there and works even when somebody refactors our software.