Is it a matter of convention that 24 September 2017, 17 September 2017, 10 September 2017, 3 September 2017, 1 February 1970, etc. are or were Sundays? Of course, we could have given and can give them a different name. They actually have different names in different languages. We could even have no common name for them. There could be no English language. There could be no Gregorian calendar (at least it could be that no one invented it). And, of course, what people do with Sundays varies greatly from one place or time to another. But it seems to me that it is no convention that these days were, are or will be Sundays. In any case, these thays would always be Sundays.

I presume that anything you would count as a Sunday must recur every seven days and must be the same day of the week. If not, then I don't know what you mean by "Sunday" in your question. But the decision to treat one week as consisting of seven days is entirely conventional rather than natural. (Notice that neither the solar year nor the lunar month divides equally into seven-day weeks.) See this link. According to other conventions, one week consists of more or fewer than seven days, so no particular day of the week recurs every seven days, so no day of the week is a Sunday.

Read another response by Stephen Maitzen
Read another response about Time