What is the origin of "Breaking in" as in a shoe or glove?

I think it probably is an extension of the earlier transitive usage of “break in” meaning teaching or training someone to do a new job, on the notion of “training” your new shoes till they become more confortable.

Break in :

• Train or instruct someone in a new job or enterprise, as in Every semester she had to break in a new teaching assistant. [Late 1700s]

• Loosen or soften with use, as in It takes a while to break in a pair of new shoes.

(AHD)

The expression appears to be from the second half of the 19th century; the earliest example I could find is from a 1867 edition of "A Japanese and English Dictionary"

• to break in a new pair of sandals.

I always thought that it came from the fact that, by using the thing more, you are breaking down and stretching out the materials of the object, making it more comfortable because now it's been appropriated for your foot, hand, etc. Don't quote me on that though, just a guess.

It most likely originates as an analogy to the process of breaking in a horse, though nowadays this appears to be more commonly known as "breaking a horse" or even just "horse training".

From What is Broke Horse? on The Spruce:

Many people don't like the term 'broke' because it suggests training done by force or by breaking the horse’s spirit. When horses were rounded up off the range and ‘bucked out’ by a rough rider who wanted to quickly make them useful, this might have been true.