Origin
The Oxford English Dictionary believes the phrase originated from children games, such as hopscotch or the board game snakes and ladders.
Speaking of snakes and ladders, the earliest recorded use of "back to square one" was from a 1952 edition of th Economic Journal. Here's the quote:
"He has the problem of maintaining the interest of the reader who is always being sent back to square one in a sort of intellectual game of snakes and ladders."
There are versions of this board game that will send you back to square one, and with the quote referencing this game to doing as such, it is possible the saying originated from there.
The other children game Oxford Enlish Dictionary mentioned was hopscotch. Hopscotch is a game that can be played by yourself or with multiple people. The course takes place on a bunch of numbered squares written on the ground, similar to a grid. Designs for the course vary.
Players throw a marker into the one square, then hop through the course, avoiding the square that contains the marker. The player hops to the top of the course and all the way back down to square one.
Finally, there's a theory that that the phrase originated from early radio commentators for football matches by the BBC in the United Kingdom. A football pitch was made into a grid that was divided into eight squares. The commentators used this to describe to those listening where the ball was located.
Examples of The Phrase Being Used
"That math test was hard, it was all greek to me."
"Listening to my mom yell at me was difficult, I couldn't make out what she was saying. It was all greek to me."
The theory was that whenever a goal kick was to be made, it would be done from square one. However if you look at the picture above, it shows that squares 1 and 2 could both be used for a goal kick, and if the other team was to get a goal kick the squares would be 7 and 8. This system was dropped by BBC shortly after it's inception. Of all the recordings that had commentators who were using this system, not once was "back to square one" heard.
Note: For most old phrases, sayings, and idioms, finding the exact person or date in which a phrase was originated is impossible. What's provided is the earliest known date the phrase or saying was being used in.
Usually the phrase is a quote from an old newspaper, book, poem, play, etc. If it is already being used by a newspaper though, then the saying must already be common knowledge among the people of that time. This means the origin of the saying is older.
For instance, if someone or something from 1660 is being quoted using a particular phrase or saying, you can assume that the saying must be older, as it's already popular and being commonly used in 1660. How far back varies from phrase to phrase.
There are some cases though where determining the origin from an exact person is possible, however these are not common. In short, most of the origins for these sayings give you a date so you can get a rough idea on when these phrases were being used.
