January 1970 in the U.S. began the widespread practice of the Saturday Vigil Mass. I believe there had been studies regarding it since the 1950s and even earlier, and the decision was actually made in 1970.
The opportunity for Catholics to attend the Saturday vigil Mass for the Sunday obligation has its roots in Jewish tradition. For Jews, a day does not start at 1 minute past midnight; a day starts at sundown and continues to the following sundown. When you read Genesis you will note that it says, "evening came, then morning. . .the first day. . .second day. . .etc. The day ‘starts’ with the coming of evening.
Now it is arbitrary to establish a time of 5 p.m. as ‘evening’. After all, in summer in many areas, sundown does not occur until later. But unless we had Mass times changing continually all year long (not practical), we can go with the earliest time average, which is about 5 p.m. for most places most of the time.
Basically the 20th century saw a huge increase in the numbers of people who ‘had to’ work on Sundays. Thus, the Vatican studied the question, proposed by the bishops, as to what could be done. Careful study and prayer, and guidance by the Holy Spirit, led to the pastoral decision that after a certain time (designated 'sundown) on Saturday, a Mass (which would normally be the vigil, or ‘anticipated’ evening Mass) would meet the Sunday obligation.
Since in the time of Christ and the first Christians, the Jewish community which were the first converts to Christianity would have considered a day to ‘begin’ at sundown, and since their own worship practice for sabbath had service start at sundown Friday evening (though the Sabbath itself was Saturday), it seems logical to conclude that a Christian service after Saturday sundown could likewise be seen as one that would have been considered by Christ Himself to meet the “Sunday” or “Lord’s Day” obligation. And thus the decision was made to offer this, which is very helpful for many people who cannot make a Sunday Mass (for various and good reason) but can make it on a Saturday evening.