Sunday is the first day of the week and Saturday is the seventh. That conforms to a tradition that goes back at least to ancient Jews long before Christianity.
It should be noted that other ways of counting and grouping days did exist concurrently to Jewish / Christian traditions. Egypt used the decan (ten days), the Roman calendar used the nundial cycle of eight days to a "week", the French Republican Calendar used ten day weeks as well (with the tenth day replacing the Sunday "as the day of rest and festivity"). The Soviet calendar was a mess, with five day weeks (with the "day off" being assigned differently to worker groups to have 80% of the work force in the factories each day), and later, six day weeks (with the last day of the week being the "day off" for everyone).
And quoting from Sunday or Monday? (which I would recommend reading in full as it showcases several, sometimes differing, views):
According to Webster's Ninth New Collegiate Dictionary (1983), the term 'weekend', first recorded in 1878, refers to 'the period between the close of one working or business or school week and the beginning of the next'. This concept firmly places Sunday at the end of the week.
Also, Wikipedia "Workweek and weekend" states that...
The present-day concept of the relatively longer 'week-end' first arose in the industrial north of Britain in the early part of nineteenth century and was originally a voluntary arrangement between factory owners and workers allowing Saturday afternoon off from 2pm in agreement that staff would be available for work sober and refreshed on Monday morning. The Oxford English Dictionary traces the first use of the term weekend to the British magazine Notes and Queries in 1879.
So precedent existed.
Mention was made in comments of the German DIN 1355 (1943) and DIN 1355-1 (1975), the former identifying the beginning of the week as "Sunday 0:00" and the latter identifying Monday as the first day of the week. This would bracket the "when" of the change, for Germany at least, as "sometime between 1943 and 1975".