There are probably multiple ways to solve this...

Here's an approach I'd choose (note that I do not use Alexa, so my knowledge about the integration's capabilities is limited):

1. define an input datetime used as an alarm time.
2. allow Alex to manipulate this input datetime
3. use a template trigger to compare the current time with the defined alarm time - and yes you can do calculation; e.g., automations triggers when current time = (alarm time - 20 minutes)
4. trigger the alarm from within home assistant by either using a delay in the same automation or use a separate automation triggered at alarm time.

I gave podman a try a few months ago and went with systemd unit files instead of compose files, since it felt like the most native approach.