In Hebrew minset, "the first of weeks" refers to the Omer count... There are seven Sabbaths... and the first is the first Sabbath after Passover.
'FIRST OF THE SABBATHS'
The proper translation of the Greek is 'first of the sabbaths'. This text could in effect be translated in a number of ways without totally destroying its meaning;
'first of the weeks'
or 'first of day of the sabbaths'
or 'first of day of the weeks'.
Deut 16:9 You shall count seven weeks for yourself; begin to count the seven weeks from the time you begin to put the sickle to the grain. 10 Then you shall keep the Feast of Weeks ...
This seven week period was followed by the annual celebration called the 'Feast of Weeks'. In the New Testament this feast is known by the
name 'Pentecost'.
The day which initiated the period of the counting of 7 weeks, and also the 50 days, was the day the wave sheaf offering was presented.
Lev 23:15 And you shall count for yourselves from the day after the Sabbath, from the day that you brought the sheaf of the wave offering: seven Sabbaths shall be completed. 16 Count fifty days to the day after the seventh Sabbath; then you shall offer a new grain offering to the LORD.
The day the sheaf of the wave offering was presented was; ** the first day of the Sabbaths **
The day a provision was to be made for the saints (1Cor 16:2). This was a specific collection of food and was to be made from any food remaining from the prior years harvest. That is why the timing, it is the first day of the new years harvest.