Not exactly.
It's true that in some of the texts, it indeed says "first of the WEEKS [/sabbathS (plural)]"
... but in those cases it is actually referring to the first of the "set of weeks" counting FROM Firstfruit [always on a Sunday] TO the day before Shavuot/Pentecost [which is also always on a Sunday], a set of seven weeks/sabbaths [complete] (that was to be "numbered")
... IOW, those "weeks" (set of seven weeks/sabbaths, plural) START on a Sunday (namely, on Firstfruit) [day one of 49], and this is what is meant by the phrase "the first of the WEEKS [/sabbathS plural]" (a very specific set of weeks/sabbaths within any given year).
In another phrase, "every first of the WEEK [singular, sabbatou]," I believe refers to the first of an actual week (any given "week" of a year, not the specific "set of seven" [btwn FF & Pentecost] like the other phrase means). This ['week'] also refers to the entire "week [singular]," thus the "first" of that would also be a Sunday (though starting "the evening before, at sundown," according to Jewish reckoning, I suppose, but the bulk of the "first [day of that 'week']" would fall on the Sunday part, see.
For example, what the bible calls the first day of the week and thus justifying meeting on Sunday is in actual fact the first of the sabbaths which as we know is on Saturday. And I am not into speaking just because I like the sound of my voice.