They really did have constitutions back then. Substantial constitutions. With many many many documents over hundreds of years.

  A constitution, or supreme law, is the aggregate of fundamental principles or established precedents that constitute the legal basis of a polity, organization or other type of entity, and commonly determines how that entity is to be governed. [0]

Their entire history of implementing and applying principles of Roman Law and other creeds was their ever growing constitution.

> The USA is a new country, and its constitutional rigidity

and general loudness on the matter of "what is a constitution and why ours is the first and the greatest" has caused much confusion given they have such a short and barely evolved one.

[0] https://en.wikipedia.org/wiki/Constitution