Any electronic shift AT trans experts in here?

I'm a Subaru mechanic and newer stuff like that should have a code if the solenoid is stuck. I can't say 100% for a Mazda but it sounds like a mechanical issue to me. No codes means the TCM is getting all the correct inputs and outputs but still no first gear action. Also, even if it's actually just the solenoid, you might look into parts availability. Subaru stopped selling solenoids when they went to CVTs in the early 2010s, now you have to buy the whole valve body for close to $1000.