The tradition of all caps denoting shouting arose from typesetting of printed publications.
The 6 September 1958 Bookseller: The Organ of the Book Trade says:
It [a 16 page list of books] picks out titles in red, and speaks moderately with large-size upper and lower-case letters rather than shouting with all caps. The effect is pleasing to anybody in a contemplative mood.
And more than a century before that, in "The Dutchman Who Had the Small Pox" in the 17 April 1856 Yorkville [South Carolina] Enquirer and many other newspapers:
This time he shouted it out in capital letters
Likewise, "The Sore Grievance of John Wellspanked" in 6 May 1871 The Shamrock says:
"TWELVE shillings and SEVEN pence?" roared my aunt in the biggest capital letters
Similarly, "Imaginary London" in the June 1873 Belgravia says:
'...Here, cab, cab, CAB!' The last monosyllable was a yell to which only capital letters can give due impression
Even more clearly, the 1880 The Standard speaker and elocutionist has a section of the book titled:
This will be seldom needed throughout an entire piece, but wherever the words imply calling, or commanding, it will be in keeping with the words to employ it. As examples note the following selections marked in CAPITAL letters as the appropriate place for shouting emphasis.
The 1880 book then goes on for pages with examples from literature of all caps being used for shouting.
However, the earliest indication of a standard that I have found so far is from the 1852 Singing for Schools and Congregations: A Grammar of Vocal Music:
It is proposed that-
CAPITAL LETTERS, in printing, or double lines under the word in writing, should distinguish words to be sung louder
Another clear example is from the 1860 Elementary books for Catholic schools, explaining how to read stories with italics and all caps:
when you come to a word printed in this way [italics], you must read it more distinctly than the other words.
...And began to scream out as loud as he could,| "HELP!HELP!HELP!"
Observe these last three words: they are printed in capital letters letters because they are very important. The man cried, "help!" very loudly.