You would need to send the SoundDock audio (approx.) every half hour to keep it alive, nothing loud that you'd notice, just something that the system would recognise to keep it alive. Does anyone know if this is a feature found in the Dot's settings? If so this will be the easiest solution.

If not, there appears to be a few other ways to do this:

1. There is a skill called "KeepAlive"
   https://www.amazon.com/Warren-Ashburner-KeepAlive/dp/B07G7WNZJF
2. Some 3rd party dock adapters specifically state that they are designed to work with the "Echo Dot". So they should keep the system alive and prevent it from going into sleep mode and should work with anything else to keep the system alive when not in use:
   https://www.amazon.com/DockLinQ-Bluetooth-Adapter-Receiver-Sounddock/dp/B07G3653DF
   https://www.amazon.com/ZIOCOM-Bluetooth-SoundDock-Connector-Lightweight/dp/B082D9YK8W
   https://www.amazon.com/Sounddock-Input-Converter-Adapter-Cable/dp/B07JW44BXG
   1. Know that unlike all later models which charged using the 30-pin USB pins, the SoundDock series I v1 charged using the 30-pin FireWire pins
      https://bose.fandom.com/wiki/SoundDock_speakers#Comparison_of_functions
      So if you find that you purchase one of these Bluetooth/Aux adapters and it does not power on, it is not designed to work with the first generation SoundDock system.
      1. USB charges with 5v on Pins 16 & 23; while Firewire charges with 12v on Pins 19, 20, 29, & 30
         https://apple.fandom.com/wiki/30-pin_dock_connector
3. Modifying the system in some way to prevent the auto shutoff feature as it appears this cannot be disabled as it was originally designed by Bose.
   https://www.instructables.com/Bose-Series-I-Sounddock-Bluetooth-Conversion/

https://www.amazon.com/DockLinQ-Bluetooth-Receiver-Compatible-Sounddock/dp/B07G3653DF/

I’m not recommending this specific one, but something like this should work.