One often hears of "the thirteen colonies", and of course the colonies were also called "provinces". Were they also sometimes called "states" before the Continental Congress convened?
The governor's Council, also known as the Council of State or simply the Council, consisted of about a dozen of colonial Virginia's wealthiest and most prominent men. Beginning in the 1630s the Crown appointed Council members, although from 1652 to 1660 the General Assembly elected the members. Crown appointments were lifetime appointments. Encyclopedia Virginia
I cannot find any mention of the colonies using the term "state" in the period 1763-1774. I recall an anecdote that George Washington used the term during the seige of Boston, but I cannot (to my great frustration) provide a citation.
One comment raised the question whether this was important: I believe it is, and I'm going to digress for a moment to lay out my opinion as to why. One of the enduring questions of the American Revolution is how the inhabitants transformed from Englishmen to Americans. At what point and by what means did they conclude that it was no longer possible to reach an accommodation with Parliament? The terms "colonies", "provinces", etc., indicate that they perceived themselves to be subjects of the Empire. Terms such as "state", "commonwealth" and "republic" indicate a disposition towards independence. Thus the first use of "state" (or a synonym) is an indicator for the transformation towards independence.
The following material I believe is not responsive to OP request, but may serve as context. (although it is not responsive to the question, sometimes it is useful to fill in the space around the question)
The first use of the term "United States" is described here
Reed was a colonel in the Continental Army and George Washington's secretary. In January 1776 Reed was on leave in Philadelphia when Moylan, who was filling in for Reed, wrote to him and said that he wanted to go to Spain on a mission to seek help for the fight against Britain “with full and ample powers from the United States of America.” There it is, the earliest documented use of the phrase “United States of America,” in a letter written by Stephen Moylan.
Thomas Jefferson used the term "American States" (hat tip to @Called2Voyage). but this is both dated 1774 and a reference to the union, not to an individual state per se.
Thomas Paine referenced the "United States of America" on 6/29/76. and in Common sense (January 1776)
"A Planter" uses the term (although the Paine advocates would take particular notice of the capitalization):
“What a prodigious sum for the united states of America to give up for the sake of a peace, that, very probably, itself would be one of the greatest misfortunes!” – A PLANTER
OP points out, "Vermont, which was not one of the thirteen colonies, but which issued its separate declaration of independence in 1777, was, during the years before its admission to the Union in 1791, most often called the "State of Vermont" but sometimes the "Commonwealth of Vermont" and I think less frequently the "Republic of Vermont". Some 20th-century historians started using that last term to refer to the status of Vermont between its declaration of independence and its admission to the Union. However, that was not during the colonial era."
The Carolina Charter of 1663 ". . . do grant full and absolute power, by virtue of these presents, to them the [Lords Proprietors], and their heirs, for the good and happy government of the said province, to ordain, make, enact, and under their seals to publish any laws whatsoever, either appertaining to the publick state of the said province". Now, this mention of "state" is as in "condition", but that is what the term "state" to refer to a political entity grew out of Source. (hat tip to @called2Voyage again!)
At this page we read:
The British North American colonies occasionally were called states as far back as 1630s;
Just a small data point. This should not discourage others from posting further on this.