When was the cricket box groin guard first used?

Answer 1

Its certainly not as late as not 1874 - apparently that is ice hockey!

With round-arm Bowling coming in from the 1820s, and overarm from the 1860s it is vanishingly unlikely that cricketers would have waited until 1874 before doing anything to protect themselves from a rising ball at (or a few inches below) waist level. After all, every other time of protection (leg pads etc.) was well in place by the early 19th century. Even 18th century underarm bowling was very fast, and could to bounce high, especially given the less then level ground.

The invention of the device would be lost in time. Various sorts of padding would have been used originally, but there is an undated and maybe apocryphal story from John Nyren's time (Hambledon, mid-late 18th century) of a player devising something made of metal that "rang like a bell" every time is was hit (to his embarrassment, it seems).

By Victorian times boxes would be made of light aluminum with some padding on the edges, replaced by plastics from the mid-20th century.

The first recorded head protection is Patsy Hendren's from 1933, though we do not see a full helmet until Dennis Amiss around 1977-78.