I wonder if he's responding to your going out, rather than being out - if that makes sense?
Some dogs can start to associate all the normal signs of you preparing to go out with being left alone and I wonder if that might be the case here. Once you're gone he's able to settle himself down - which is great.
I think if he were mine, I would firstly video him while he was left alone - just to be absolutely sure he is fine for the duration he is being left and it's just the first few mins that are difficult.
Assuming that is the case, I'd be attempting to desensitise him to the leaving ritual by repeating little bits of it even when I wasn't going out. E.g. ut your shoes on, give him a treat, take them off.
Put shoes and coat on, treat, take them off.
Put shoes, coat and radio on, treat, take/turn them off.
So long as he didn't show any signs of anxiety you just keep adding bits of the routine in. If he gets upset even at just shoes going on then break it down even further (e.g. just touching the shoes).
Repeat until he accepts the 'getting ready to go out' routine as just another ordinary occurrence that may/may not lead to you leaving.