How do you use that to predict which atom decays next?

The decayed state exists, it's the second term sqrt(exp(-t/T))|0>

How do you predict which atom decays next from there?

Since the decayed state exists, then any. Your question tries to assume sqrt(exp(-t/T))=0, which is false.

My point was that we cannot predict which atom decays next.

If you want to claim that we could predict which specific atom decays next, I'd really like to see a lot more explaintion and exposition as it would upend current understanding.

The trick is that you can't predict something that doesn't happen even if you feel otherwise.

Atoms don't decay? Radioactive decay isn't a thing?

But at least we agree there is nothing we can predict.

We can predict decay process as

sqrt(1-exp(-t/T))|1> + sqrt(exp(-t/T))|0>

I give you ten atoms of Po210, you tell me which one will be next to turn into Pb206. What's your algorithm to do that?

My algorithm is at least to not predict it as not what it is. All ten atoms decay according to the formula above.