The name
Ontarí'io comes from Wendat, the language of the Wendat (Huron) people, one of the Iroquoian languages. It is generally analyzed as combining a root for “lake” — related to forms such as ontar- or yǫtáreʔ — with a suffix meaning “great” or “beautiful”, -io / -'io. Exact spellings and morpheme boundaries vary across sources and dialects.
The usual glosses are “great lake” and “beautiful lake”. “Sparkling water” and “beautiful water” are more often linked to related Iroquoian forms such as skanadario or kanadario, while the Wendat Ontarí'io-type form is most often read as “great” or “beautiful lake”. The senses overlap, and all of them point at the same idea.
The Kanien'kéha (Mohawk) form is Kaniatarí:io. The Chiefs of Ontario have cited Oniatarí:io and related forms including Kanadario.
Europeans came to it late. They were applying “Ontario” to the lake by the 1640s. Nicolas Sanson's influential 1656 map is among the earliest to show the Great Lakes in recognisable form, and labels this one Ontario, ou Lac de St. Louys. By around 1660 François Du Creux (Creuxius) was using Lacus Ontarius, after which the Indigenous-derived name predominated.
So the date on these garments is a settler timestamp, and we know it. The lake did not begin in 1656. It was named, and known, and travelled long before anyone drew it.
The north shore of the lake is the traditional territory of the Mississaugas of the Credit. Its watershed is also Haudenosaunee and Wendat homeland. Everything here is printed in Mississauga, within sight of the water it is named for.