It should work, although most of the USB to 3.5 adaptors seem to be meant to go the other way, I'm not sure they'd work here.
Also, don't forget that most sound systems with DAB also have Bluetooth receivers, you could connect the Alexa to the stereo that way. I've done both the 3.5 and Bluetooth approach before.
Simplest? Depends if people remember to switch the input on the stereo after they use anything other than the Alexa. And it also means that the Alexa won't be usable whenever any other source has been selected. Because Alexa will continue to send all your audio out down the 3.5 even if the receiver isn't listening.
You can get past that with something like a Logitech harmony remote, but even that's a bit naff.
The simplest is to abandon hope of using CDs and go full streaming. Some services used to let you upload your own CDs as well as anything you've paid for (Google Music, now replaced by YouTube music). Internet radio completely replaces DAB, streaming can cover CDs, everyone is happy (but might be paying more for the subscription to a streaming service).