First settled by Etruscans

Mantua is widely believed to have been founded by the Etruscans. According to Etruscan tradition, the city was "re-founded" by Ocno (also known as Bianore), a legendary figure. Furthermore, the city's name, Mantua, is thought to derive from Mantus, an Etruscan god of the underworld, similar to the Greek Hades.

The place where the square is built was already used by the Etruscans.
See fr.wikipedia.org

"The two necropolises constitute a unique and exceptional testimony to the ancient Etruscan civilisation" (OUV)

(...) a series of excavation campaigns has brought to light on the Poggio Civitella, near Montalcino, the remains of an imposing Etruscan fortress which is one of the first buildings of this type identified and the only one unearthed so far. (Nomination file, p. 52)
See it.wikipedia.org

For a period in the 6th and early 5th centuries BCE, Pompeii was a member of the Etruscan League of cities, indicating its political and cultural alignment with the Etruscan world. Excavations in Pompeii have revealed Etruscan inscriptions, particularly on pottery and votive offerings in early sanctuaries like the Temple of Apollo.

"Florence was built on the site of an Etruscan settlement and the later ancient Roman colony of Florentia (founded in 59 BC)." (Official description)

Etruscan necropolis of Spina near Comacchio