I have been having the same problem for some time: First shot of the day runs much slower than the second.

Background:

Breville Oracle Touch machine (double boiler, PID)
Originally using built in grinder and auto-tamper
Since moved to Lucca Atom 75 and WDT/manual tamping.
Problem seems to be worse with medium dark supermarket beans (no understanding why this would be) vs. local medium fresh roasted.
I do purge about 1/2-1G of coffee out of grinder each morning.
Pulling 1:1 for medium dark and 1:1.5 for medium beans
First shot will run about 33 seconds, then the second will be about 20 seconds or so.

So impossible to dial in grinder more accurately because either first takes 50 seconds to get the second to be 27 or the second runs out in 15-20 seconds.

I feel my puck prep and tamping is pretty solid.

Would machine variance from one shot to another be a reason for this? I'm just very frustrated. Thanks for any comments.

Those super market beans are probably stale. Best by dates are useless. Always look for roast dates and if it is post two weeks from roast or more it probably isn't worth buying. But if you have no choice but to get the market beans on occasion grind them finer than you would think to. Each day drop it a little finer until it no longer helps. At that point flip it to turbo coarse and run quick.

Between shots do you rinse the portafilter and then reload for the next shot or rinse and dry before reload? Water in the portafilter with the grounds can cause this effect by expanding the coffee and leading to channeling and faster run times. This is a very common issue as people are learning the skill set.

That atom 75 probably needs a longer purge than .5 to 1 gram. Probably more like 2 or 3, possibly more.. Big flats have big retention.
My Macap is a 58mm and it retains 2 to 3 grams everytime. Take the good with the bad.

+1 for drying the portafilter after rinsing it - my second shot time would be consistently materially quicker if I didn't do this.

Retention in the grinder.
Purge a gram or two before the first shot

Ok the consensus seems to be grinder retention, but this grinder claims to be low retention (don't they all). I'll try tossing a full 2G tomorrow and see if it makes a difference. That would be really painful with expensive beans but right now we've got some Sam's club special in there.

I do dry the portafilter - didn't mention that.

I understand the beans are not ideal or fresh, but don't see how that would make 1st vs. 2nd cup so different.

Will report back.

Plenty of evidence that the retention is several grams. See, for example, Lucca Atom 75 Espresso Grinder Review

I'd try 5-10 g if not more.

sounds similar to my df64 retention+regrinding issues with stock declumper. clearing grinder before next pull fix that. there's usually 2g+ left.

i dont have atom, but i'd also bet on retention. i also expect more than 2g+ since you cant bellow it. if you maybe dont like purging,
try 3rd shot see if its similar to 2nd.