Any way to connect Echo Dot to a Bluetooth DAC?

I have Echo Dot Max and I’m trying to connect it to the SMSL C200 DAC over Bluetooth, so I can tell Alexa to play music on the external speakers connected to the DAC.

The problem is that Alexa app and Echo Dot Max (when I say “Pair Bluetooth“) don’t see the DAC, while my iPhone and MacBook connect to it and play through it perfectly.

I made sure neither iPhone, nor MacBook are connected to the DAC at the time of Alexa pairing attempts. I have tried factory resetting the DAC for the hell of it. But nothing works.

Is there something else I can try, or Alexa/Dot are just buggy?