Romans built large scale concrete structures in months, not years. Given that these would require a great many layers of cement, not just one, the upper bound for curing time would have to be several days, a week at the very edge of possibility.

Keep in mind that concrete usually isn't allowed to fully cure before construction moves on. Most concrete houses only fully set after 2-3 years and truly large structures, famously Hoover dam, can take centuries.

They probably overbuilt so that the half cured concrete would support the structure. Hence it's still around 2000 years later.

Look at the old railroad bridges and viaducts built in the 1890s that are still going strong. They continue to exist because they are grossly overbuilt.

This is why Hoover Dam was poured in planned, interlocking segments, with cold water piped through it to accelerate curing.

A contiguous pour would have taken an estimated 125 years to cure, even assuming no fatal shrinkage occurred.

Surely cooling retards curing. And it is commonly done to avoid inducing thermal stress and causing cracks.

Not necessarily - the reaction that produces heat is purely chemical, by taking this heat away you're not going to stop it, but you are going to give more headroom for the reaction to continue.