The click has nothing to do with the MCU or the DAC; it is inherent to your way to start playing sound. The only configuration issue could be the position of the “idle” output: it must be at the middle of the output range (thus corresponding to “no signal”); otherwise you will get a steep front (thus a click) when switching even to no-signal waveform.
However even in this case you will still hear a click if you start playing sound at full volume immediatly as going from no-signal to full-signal (even a sinus waveform), when converted in frequency space will have a wide spectrum at the beginning, heard as a click by your ear. Note that this artefact can be heard even on some high quality devices (like Bose Quiet-Comfort noise reducing headphones...)
The cleanest way to suppress the click is thus to start playing your waveform at 0 volume, then raise it progressively to full volume in a few hudrends of milliseconds.