Did early Italian immigrants eat it?
At what point were there Pizzerias in New York?
At what point was it something non-Italian-Americans would be familiar with?
At what point was it something they'd eat regularly?
"Pizza" in a rudimentary form has been around since Roman times, though for most of its history, it basically just meant a flat piece of bread with ingredients baked into it.
According to the Oxford English Dictionary the word "pizza" first appeared in the English language in John Florio's 1598 Italian-to-English dictionary A worlde of wordes, or most copious, and exact dictionarie in Italian and English, where "pizza" is given the definition:
"Pizza,..a kind of cake or simnell or wafer"
References to this "cake" appeared throughout the 19th Century in English, but it wasn't until near the turn of the century that one of pizza's essential ingredients as most people would understand it today—tomato sauce—was introduced to the dish. For example, this 1878 description from Dolce Napoli by W.J.A. Stamer doesn't mention tomatoes at all:
"Anoint [dough] profusely with oil of olive, and dab in pieces of garlic, anchovy, strong cheese, rancid bacon, and whatsoever else may be highest in flavour and lowest in price; put into a hot oven, bake, and thou hast pizza."
That's probably because Europeans were rather reluctant for a long time to eat tomatoes, considering them poisonous, and they weren't really popularized until the mid-19th Century. At least, that's the case in England, the U.S., and Canada. I do believe they had come into regular use in Italian cuisine by the end of the 1700s, but someone with more expertise in Italian culinary history can correct the date if I'm off. Regardless, it wasn't until the mid to late 1800s that pizza in Italy was being prepared with tomatoes. One of the earliest such descriptions, comes from Carlo Collodi's Il viaggo per l'Italia di Giannettino, an 1882-86 anthology written for schoolchildren:
"Do you want to know what pizza is? It is a flat bread of leavened dough, toasted in the oven, with a sauce of a little bit of everything on it. The black of the toasted bread, the off-white of the garlic and anchovies, the greeny rellow of the oil and lightly fried greens, and the red bits of the tomatoes scattered here and there give the pizza an air of messy grime very much in keeping with that of the man selling it."
In the United States, Lombardi's in New York City is generally credited with introducing the pizza to Americans, in 1905, according to the New York Times. From the get-go, it appears that the dish featured tomato sauce as a key ingredient. The dish quickly spread in popularity throughout that city: Totonno's Pizzeria was opened on Coney Island in 1924, John's on Bleecker opened in 1929, and Patsy's in Harlem opened in 1933. By then, pizza was being sold by the slice in various restaurants, with John's famously hanging a sign in their window: "No slices".
Though to out-of-towners, and even borough-dwellers, it was still a foreign enough food that the New York newspapers were writing articles in the 1930s and into the 40s in somewhat exotic terms. The Jan 21, 1935, edition of the Brooklyn Daily Eagle wrote this short article about a pizzeria on the West Side of Manhattan:
"Another candidate for the new edition of 'Going Places' is the Pizzeria alla Napoletana, an Italian restaurant at 147 W. 48th St., which is rapidly becoming famous for 'pizza,' a dessert that dates back to the early Romans. Pizza requires a special type of oven with the flame coming down from the top, which explains why it is so hard to get in the majority of the restaurants that cater to the Mussolini trade...
"We were introduced to pizza the other [morning] and if your tastes run to cheeses you'll find it a delight, just as we did. It is baked in a great big shallow dish almost as large as a tea tray. And it is served in triangles, like slabs of pie.
"Pizza, as properly prepared, is baked cheese and tomato. Another version consists of cheese, tomatoes, olives, and anchovies all baked together. So tasty! People polish off whole platters of it at a single sitting.
"Pizza is much like pie. Americans often order it by asking for pie. You can combine both techniques, however, by asking the waiter for 'a pizza pie.' (Some pun, hey kid?)"
A 1943 article in the New York Times wrote of pizza available in Greenwich Village, and spelled it out for the readers that the term was pronounced "peet-sa". The September 20, 1944, edition of the same newspaper profiled the same Manhattan pizzeria that the Brooklyn Daily Eagle had a decade earlier:
"One of the most popular dishes in southern Italy, especially in the vicinity of Naples, is pizza--a pie made from a yeast dough and filled with any number of different centers, each one containing tomatoes. Cheese, mushrooms, anchovies, capers, onions, and so on may be used. At 147 West Forty-eight Street, Luigiono's Pizzeria Alla Napoletana prepares authentic pizze [sic], which may be ordered to take home. They are packed, piping hot, in special boxes for that purpose."
The May 25, 1947, edition of the New York Times featured a recipe for pizza, and declared, "The pizza could be as popular a snack as hamburgers if only Americans knew more about it."
Prophetic words, because by then, pizza had begun its rise. The dish had spread throughout the Northeast and other major urban centers in the United States. The August 29, 1939, edition of the Detroit Free Press profiled an unnamed Italian bakery, describing to their readers exactly what the dish was, and saying it could be ordered ahead of time from the bakery and delivered to your door:
"Call your order the evening before and have the pizza brought to your doorstop, hot and ready to serve when you want it. A huge one--enough for at least 25 guests--sells for $1. You can get them in halves for 50 cents."
Similarly, the Hartford Courant in Connecticut featured ads by De Pasquale's Restaurant and Pizzeria for New Year's 1941, offering free delivery of spaghetti and pizza until 3am that evening. The pizzeria was mentioned for several years after in the same newspaper.
And Bostonians were familiar with the dish by then too. The first credited appearance of the term "pizza oven" in English is given to an ad that appeared in the Oct 30, 1937, edition of the Boston Globe, which read:
"Hearth fired Pizza oven, slightly used; will set up, ready to bake."
By the end of the 1940s, pizza had started to become ubiquitous in the U.S., and also the pizza delivery business had begun, with Di Salvo's Pizzeria in Wilkes-Barre, Pennsylvania, running regular ads in the local newspaper by mid-1948.
In 1960, a pizzeria in Ypsilanti, Michigan, called "Dominick's" started their delivery business, aimed at students at Eastern Michigan University. They opened locations in Ann Arbor (home of the University of Michigan) and Lansing (home of Michigan State University) by the end of the 1960s, by which time the chain had changed its name to Domino's. By the end of the 1970s, they had hundreds of locations throughout the United States. Pizza has been an American staple ever since.