Milk toast (or milk-toast or milktoast) as a bland, nutritious, easily digested food is mentioned at least as far back as 1884. Maria Parloa, The Appledore Cook Book: Containing Practical Receipts for Plain and Rich Cooking (1884) has this entry under "Miscellaneous Receipts":
Milk Toast. Put one quart of milk in a tin pail or basin, and set into a kettle of boiling water. When it comes to a boil stir in two spoonfuls of flour, mixed with half a cup of milk, one spoonful of butter, and salt to taste ; let this boil ten minutes, and then put in the bread, which must be toasted brown. Cook five minutes longer and serve.
And Kurt Heppe, Explanations of all terms used in Coockery-Cellaring and the preparation of drinks (1908) offers this alternative definition:
Milktoast— bowl filled with toast and covered with boiling milk; terrapin plate; serve milk separate.
Milktoast has long been a recommended dietary element for very young children. Thus, in Isaac Burney Yeo, Food in Health and Disease (1890), we find these recommendations under "Schedule of Infant-Feeding":
Diet from 18 months to 2½ years. ... 4th meal, 6:30 p.m.—A breakfastcupful of milk, a slice of soft milk toast, or a slice or two of bread and butter.
[Diet for children up to the age of 3½ years] ... 4th meal, 7 p.m.—A tumblerful of milk, and one or to slices of well-moistened milk-toast.
[Diet for the rest of childhood] ... Supper. Daily. Milk. Milk toast, or bread and butter. Stewed fruit.
This association with infancy no doubt contributes to the pejorative tone of milktoast or milquetoast when applied to an adult. As others have noted, the cartoon character Caspar Milquetoast appeared in H. T. Webster's "The Timid Soul" one-panel strips starting in 1924. Most early instances of "a milquetoast" that a Google Books search returns capitalize the M in the word.
The phrase "a Caspar Milquetoast" appears in four different Google Books sources from 1939—the American Institute of Architects' periodical The Octagon, Florence Finch Kelly's Flowing Stream: The Story of Fifty-six Years in American Newspaper Life, Livingston Harley's Our Maginot Line: The Defense of the Americas, and Motion Picture Review Digest.
The earliest appearance of the phrase "a 'Milquetoast'" in Google Books search results is in Robert Bales & Talcott Parsons, Family: Socialization and Interaction Process (1956):
An example we may take a case reported in R. W. White's Abnormal Personality [citation details omitted]. The patient repressed his own sexual timidity, and his deviant sexual wishes. This allowed him to conceive of himself as an exceptionally fine person; one whom the world should praise. But, instead of praising him, people around tended to treat him as something of a 'Milquetoast' character. He explained their treatment by constructing a delusional system (which eventually hardened into a complete rationalization of life) where in there was a conspiracy on the part of these others to control him, and confine him, for devious purposes.
And "a Milquetoast" (without quotation marks around the name) appears a year later in The Lasting South: Fourteen Southerners Look at Their Home (1957) [snippet]:
He moves, when he moves at all, with grudging slowness. He is a Jeremiah forever wailing in the habitations of the wilderness, a wet-blanket, a Milquetoast, a bore. Or in another version, beloved of Mr. Block of the Washington Post, he is a fat and bloated fellow, unjustly rich (you know he is unjustly rich because he is smoking a cee-gar)
But instances of "a milquetoast" with a lowercase m appear in 1958 in The Annual Survey of Psychoanalysis, in Best's Insurance News, in the United Steelworkers of America's Proceedings of the Constitutional Convention, and in New York Theatre Critics' Reviews.
Instances of "a milktoast" are even earlier, starting with Mary Harmon Lasher, Logging Chance (1944) [snippet]:
"Yes. Listen, Mike. About Boyle. He's the man behind this. I can't give you any signed-and-sealed evidence. Except this." Bob paused, fighting for breath to make things plain. "The reports would have to be juggled to cover this, Mike. Our fallers and buckers are paid by the bushel—that means they get their money for the trees they cut. Well, those figures couldn't appear on the books— they would be higher than the tally at the rafting round. You see? No one could be doing this but Boyle. No one else could manage it."
"How about the bookkeeper?" They were nearing the tug now, their heads close together. Mike played the spotlight slowly.
"He's a milktoast. Boyle tells him what to do."
Similarly, this Pitney-Bowes ad appeared in (among other periodicals) Burroughs Clearing House (1946), Dun's Review (1947), The New Yorker (1947), American Business (1948), and The Office: Magazine of Office Equipment (1948) [snippet]:
A face you can trust?
No such thing, according to policemen and psychologists! . . . The tough egg may look like a milktoast, and refined features cloak a rogue. Solid citizens and shoplifters, burglars and bishops, too often have the same face values!
Exception, your Honors ! . . . You can trust the open, honest, face of the Pitney-Bowes Mailing Scale! . . . The hairline markings, widely spaced for visibility, are carefully calibrated, leave no doubt as to the exact weight of letter or parcel — so important in this day of Airmail.
The absence of any matches for "a milktoast" in Google Books results before the heyday of Caspar Milquetoast strongly suggests that "a milktoast" as a pejorative term owes its existence to him. On the other hand, H. T. Webster didn't pull "Caspar Milquetoast" out of the thin air.
To appreciate the freighted pedigree of milktoast and milquetoast, we need to take into account the much earlier word milksop—which originally referred to "bread soaked in milk," but which English speakers began using centuries ago as an insult term for what Merriam-Webster's calls "an unmanly man."
One early instance of milksop used in this sense appears in Shakespeare's Richard III (1592):
And who doth lead them but a paltry fellow,
Long kept in Bretagne at his mother's cost?
A milk-sop, one that never in his life
Felt so much cold, as over shoes in snow.
Let's whip these stragglers o'er the seas again,
Lash hence these over-weening rags of France,
These famish'd beggars, weary of their lives ;
Who, but for dreaming on this fond exploit
For want of means, poor rats, had hang'd themselves.
Another early instance is in Beaumont and Fletcher, Love's Cure, or The Martial Maid (1647):
Bobadilla. Oh Craven-chicken of a Cock o' th' game : well, what remedy? Did thy Father see this, O' my Conscience, he would cut off thy Masculine gender, crop thine Ears, beat out thine Eyes, and set thee in one of the Pear-trees for a Scare-crow : As I am Vitelli, I am satisfied ; But as I am Bobadilla Spindola Zancho, Steward of the House, and thy Fathers Servant, I could find in my heart to lop off the hinder part of thy Face, or to beat all thy Teeth into thy Mouth : Oh thou whay-blooded Milk-sop, I'll wait upon thee no longer, thou shalt ev'n wait upon me : come your ways Sir, I shall take a little pains with ye else.
And apropos of "whay-blooded," Samuel Johnson, in one of his "Notes on the Merchant of Venice," in The Plays of Shakespeare (1771 edition), has this to say about red blood in contradistinction to milk:
To prove whose blood is reddest, his or mine. To understand how the tawney Prince [the Prince of Morocco in The Merchant of Venice], whose savage dignity is very well supported, means to recommend himself by this challenge, it must be remembered that red blood is a traditionary sign of courage : Thus Macbeth calls on of his frighted soldiers, a lily liver'd Lown ; again, in this play, Cowards are said to have livers white as milk ; and an effeminate and timorous man is termed a milk-sop.
With that lineage, it is hardly baffling to see "The Timid One" in 1924 christened "Caspar Milquetoast."