From MATTERS LITURGICAL (The Collectio Rerum Liturgicarum) by Rev. Joseph Wuest, C.SS.R.  Page 315  #180.       "The Time of Mass. b)  According to the general law Mass may not be begun sooner than one hour before dawn or later than 1 o'clock in the afternoon....c)  Dawn begins with the first appearance of daylight and ends with the first appearance of the sun over the horizon. It is however licit to begin Mass as much as one hour and twenty minutes before the beginning of dawn as astronomically determined, since only a moral computation of dawn is required." Then come a series of exceptions and comments about such feasts as Christmas and Easter and about those who have no dawn for a certain period of the year,etc.  There is nothing given about being able to start Mass anytime after midnight. This is interesting, too, because every New Year's Eve Fr. Joseph Pfieffer has a midnight Mass. He always had his reasons for this but they didn't seems solid to me.

Yes, but Pius XII dumped these restrictions entirely, and bishops regularly made exceptions for pastoral needs (e.g. to accommodate faithful who required an earlier Mass time).  This was more of a guideline than a hard-fast rule, as evidence by all the "exceptions".  I think that a midnight Mass on New Year's Eve is a great idea.  While the world welcomes the New Year with debauchery, Catholics sanctify it with the Mass.  I love it.

So PPXII "dumped these restrictions entirely" and now the liturgy rules are based on personal preference of bishops and priests?

I don't know what the rules were apart from midnigt fast but in our parish in St Dublin, Ireland, in the 1940s and 1950s there was 7,8,9,10,11 and 12 Mass. Most inrteresting was that Holy Communion was not served at 11 or 12 Mass. I recall my dad liked a pint on Saturday night and nearly always went to 12 Mass. Indeed a lot of Irishmen liked a pint or two on Saturday night so that could explain why no Communion was given on those late Masses. The most popular Mass was the 8-o-clock one. In those days I served as an altarboy so got to know these things.

During the 1950s, Pope Pius XII requested that Fr Bea, a Jesuit of course, revise the translation of the Psalter, the words of Psalm 26 that contained “I will wash my hands among the innocent” the one used for centuries in the part of the Offertory Rite of the Mass where the priest washes his hands. The last translation of this Psalm was done at the Council of Trent, yet Pope Pius XII wanted an updated translation. Fr Bea, made a cardinal by Pope John XXIII in 1959, was a liberal who also championed the modernist religious liberty at Vatican II against the religious tolerance of the traditionalist Cardinal Ottaviani causing division and rupture at the Council.

https://www.jstor.org/stable/43719062?seq=1#page_scan_tab_contents

I have been under the impression for a long time, and still am, that the earliest time Holy Mass can begin corresponds with the break of dawn or close to that moment of the rising of the sun. And, because the birth of Christ as well as His Holy Resurrection happened at midnight, Holy Mass is allowed at that time, too, (maybe almost required?) for liturgy and creation to blend beautifully.  The priest facing east while offering the Holy Sacrifice is another example of the Church's blending liturgy with the life of Christ.  

During the American cινιℓ ωαr there was mass celebrated at 4:30AM.