While you wait for a more definitive answer, you may be interested in this very old post of mine trying to figure out when pizza became a popular casual restaurant food in the United States outside of Italian ethnic enclaves.

Pizza delivery was definitely a “thing” by the 1960’s and the birth of the Domino’s (originally Domi-Nick’s) chain. As mentioned in the answer, Domino’s was an innovator in pizza box technology in the mid-1960s which I’m sure, even if it didn’t invent pizza delivery, made it easier (previously pies had been sent out with the pizza on a corrugated base that was then slipped into a bag or, at least according to some sources, “rolled into a cone, wrapped in paper, and loosely tied with twine”). However, there’s definitely more to be said on pizza delivery particularly rather than pizza’s overall popularity generally.

Pizza has been around in Italy for centuries, but for most of its history, it referred to a flatbread with toppings, mostly olive oil and spices. Fancier pizzas would have fish, meat, or cheese on them.

The addition of tomatoes, or tomato sauce, was one which didn't develop until the 19th Century, which is no surprise, because Europeans, including Italians, didn't really start using tomatoes in their cuisine a whole lot before that. The pizza we are most familiar with today as the "standard" in the United States is based off the pizza margherita from Naples, which is pizza dough topped with tomato sauce, mozzarella cheese, and basil. The American standard is a modification of this, where the basil optional, and the cheese is not sliced or dolloped, but grated, and covers nearly the whole surface.

Below is a collection of milestones in the history of pizza, as it pertains to the United States (mostly):

1830: According to various sources, in the 1830 Italian language book Napoli, contorni e dintorni ("Naples, contours and surroundings") published by an author named as "Riccio", a type of pizza is described with the ingredients "pomodoro, mozzarella e basilico" ("tomatoes, mozzarella, and basil"). This seems to describe a margherita style pizza, in Naples. This appears to be the first description of such a pizza, though it may have been around for some time before this.

1866: On page 124 of the book Usi e costumi di Napoli e contorni descritti e dipinti, Volume 2 ed. by Francesco de Bourcard, an essay by Emmanuele Rocco appears, entitled "Il Pizzajuolo" which describes pizza. (Some sources say the essay itself dates to 1849, but I can't confirm that at the oment.) The essay describes pizzas with tomatoes, cheese, and various other toppings. Translated from the aforementioned page:

"The most ordinary pizzas, called coll'aglio e l'olio [lit. "with garlic and oil"], are covered with oil, and on top is spread salt, oregano and minced cloves of garlic.

"Others are covered with grated cheese and seasoned with lard, and then a few leaves of basil are placed on top of it. First of all, small fish are often added; secondly, thin slices of mozzarella are used. Sometimes we use sliced prosciutto, or tomato, or clams, etc. Sometimes by folding the dough itself, we form what is called a calzone."

1884: According to Folklore, Fakelore, History: Invented Tradition and the Origins of the Pizza Margherita by Zachary Nowak that appeared in the March 2014 edition of the Food, Culture & Society journal, an Italian journalist named Matilde Serao wrote a series of articles in 1884 about the poor residents of Naples, in which Serao cynically described pizza as:

"made from a dense dough that burns but does not cook, and is covered with almost-raw tomatoes, with garlic, with oregano, with pepper: these pizzas in many pieces that cost one soldo are entrusted to a boy who walks around to sell them on the street, on a movable table, and there he stays the whole day, with these slices of pizza which freeze in the cold, which turn yellow in the sun, eaten by the flies."

1889: Raffaele Esposito hosts Margherita of Savoy, the Italian queen consort, at his Pizzeria Brandi in Naples. In later years, Esposito would claim that he invented the pizza margherita during this visit, specifically for the Queen Consort. According to Nowak's article, there is documentary evidence that the visit took place, but the actual claim of Esposito inventing the pizza margherita is dubious, since there are several earlier descriptions of similar pizzas using tomatoes, cheese, and basil as toppings. In all likelihood, Esposito's contribution is giving this particular style of pizza its name, as well as helping to popularize it. Esposito's claim of inventing the name didn't appear in print until the 1930s, so it's unknown if this style of pizza was truly known as the pizza margherita until that time. But Esposito's role in popularizing it does seem to have some weight: his pizzeria was (and is) on one of the main thoroughfares of Naples, unlike many others of the time, which tended to be holes-in-the-wall off the beaten path of Naples. According to Nowak, the Pizzeria Brandi was one of only three known pizzerias operating before 1900 in Naples that was still operating in the 1930s. Considering that early New York mentions of pizza often point to its Neapolitan origin, the Pizzeria Brandi has a circumstantial, if shaky, claim to being one of the pizzerias that early New York proprietors may have been taking their cues from when introducing the dish to American customers.

1897: Italian immigrant Filippo Milone opens an Italian grocery store on Spring Street, in Manhattan, New York's "Little Italy" neighborhood. The address is supposed to have been 53 Spring Street.

1901: According to the research of Peter Regas, currently writing a book on the topic, Filippo Milone sells his grocery store to fellow Italian immigrant Giovanni Santillo. While it's unconfirmed exactly when, the grocery store is said to have started selling Neapolitan-style pizzas out of its bakery around this time.

1903: An ad in the May 9, 1903, edition of the Italian language New York newspaper Il Telegrafo confirms the opening of a pizzeria at 192 Grand Street in Manhattan. The ad describes the Antica Pizzeria Port'alba as an "elegant Neapolitan pizzeria". This is the earliest known dedicated "pizzeria" in North America, rather than an Italian bakery or grocery store. It is owned and operatd by Filippo Milone, the same man who had sold his previous business two years earlier. He would end up selling (or perhaps closing) this one, too.

1905: The March 25, 1905, edition of New York's Il Telegrafo confirms the opening of a pizzeria at 53 1/2 Spring Street, with the name Antica Pizzera Napoletana, situated next door to the original Italian grocery. The ad claims the proprietor Giovanni Santillo:

"makes known to all his friends of the Italian Colony [i.e., Little Italy] that in his place they make Pizzas as made in Naples, as Santillo is a pizza maker from Naples who for a long time ran one of the main pizzerias [there]."

One of the early employees of this pizzeria was Gennaro Lombardi, who had immigrated to New York from Italy the previous year. He would eventually buy the pizzeria and operate it under his own name.

1910s: Pizza places began popping up around the Northeast. In 1910, Ianelli's opened up in Philadelphia, and remained in operation until just a couple years ago. In 1912, Papa Tomato Pie's opened in Robbinsville, outside Trenton, and remains in operation today, the oldest continuous pizza maker in the United States (Lombardi's closed down for a few years in the 1980s). Eugeno Burlino began selling a "tomato pie" with no cheese in Utica, New York, in 1914, and it continues to operate, now under the name O'Scugnizzo's. Philadelphia had a second pizza seller by 1918, Sarcone's Bakery, which also remains in business. Unlike many other historic pizza sellers, Sarcone's never transitioned into becoming a pizzeria. It has remained primarily an Italian bakery that also sells pizza.

1915: Filippo Milone, the original proprietor of the Spring Street grocery store opened in 1897, has closed his 1903 pizzeria by this point, and began operating an Italian bakery at 175 Sullivan Street. The 1916 New York City directory lists Millone at that address selling "pies".

1924: Totonno’s Pizzeria Napolitano opened on Coney Island, operated by Antonio "Totonno" Pero, which is still in business. It's the oldest pizzeria in Brooklyn, though it doesn't claim to be the first, and it's probably not. Pero had previously worked at Lombardi's; Gennaro Lombardi was probably running the kitchen at the Spring Street pizzeria by this point, if he had not actually bought the business already. The name "Lombardi's" for the Spring Street pizzeria would not appear in print for another fourteen years.

1924: According to a surviving 1940s postcard (front, back), Granato's Pizzeria Napolitana in Chicago opened this year, at 907 W. Taylor Street. If it's not the exact date, then it's close, because the 1928-29 Chicago phone book lists Joseph "Gramato" operating a restaurant at that address. This is possibly the earliest pizzeria in the U.S. operating outside the Northeast. Gramato's would continue to be a Chicago mainstay until it was closed in 1961 when the University of Illinois Chicago expanded its campus.

By 1926, Chicago would have its second pizzeria, when Italian immigrant Ferdinand Rosati moved there from Coney Island, and opened up a pizzeria at the corner of Madison and Crawford streets.

1925: By this year, Filippo Milone sold his "bakery" on Sullivan Street in Manhattan to an in-law of his named John Sasso. Sasso is listed in the New York city directory this year as operating the Pizzeria Port’Alba at 175 Sullivan Street. It's possible, maybe even likely, that the name of the "bakery" had been the Pizzeria Port'Alba since Milone opened it in 1915.

(cont'd...)