According to Merriam-Webster's Eleventh Collegiate Dictionary, the word pasta has appeared in English publications since at least 1847—but you wouldn't know it by checking editions of Webster's Collegiate Dictionary prior to the seventh edition (1963). That's when the first entry for pasta appeared in the Collegiate series, as follows:
pasta n {It[alian], fr. L[ate] L[atin]} 1 : a paste in processed form (as spaghetti) or in the form of fresh dough (as ravioli) 2 : a dish of cooked pasta
Prior to the Seventh Collegiate, the only term that Webster's offered for the generic category of (usually) eggless noodles now generally termed pasta was paste, as in this relevant definition from a longer entry for that word in the Sixth Collegiate (1948) suggests:
paste, n. 1. Dough; specif.: ... b Any shaped and dried dough prepared from semolina, farina, or wheat flour, or a mixture of these with water (as in macaroni, spaghetti, vermicelli), milk, or egg.
Because of confounding alternative meanings, there is little point in tracking the frequency of paste over the past 120 years in Google Ngram, but an expansion of the Ngram that GEdgar provides for pasta (blue line) and spaghetti (red line) to include macaroni (green line), noodles (yellow line), and vermicelli (dark blue line) over the period 1900–2019 yields an interesting set of line plots:
The most surprising thing to me about this chart is the relative newness of the word noodles: in 1900, the only word of the four track that had any significant frequency of usage in published work was macaroni.
A search through US English dictionaries yields some insight into which words were in use when and with what meanings.
Published only a few decades after the heyday of "Yankee Doodle," Noah Webster's A Compendious Dictionary of the English Language (1806) has this entry for macaroni:
*Macaroni, n. a fop, fribble, finical fellow, paste
The same dictionary devotes no space to paste in the specific sense of something edible:
Paste, n. a thick mixture of solids and fluids, a cement
Sounds yummy. Neither spaghetti nor noodle has any entry in the 1806 Compendious Dictionary, but to my surprise, there is an entry for vermicelli:
Vermicelli, n. a paste made like threds, a soop.
Webster's much larger An American Dictionary of the English Language (1828) has nothing for spaghetti, but the other four words are at least mentioned, although only one seems much related to pasta in the modern sense:
MACARONI, n. {It. maccheroni, a sort of paste ; Fr. macaroni ; Gr. μαχαρ, happy.} 1. A kind of biscuit made of flour, eggs, sugar, and almonds, and dressed with butter and spices. B. Jonson 2. A sort of droll or fool, and hence, a fop ; a fribble ; a finical fellow.
NOODLE, n. A simpleton. {A vulgar word.}
PASTE, n. {Fr. pâte, for paste ; It. Sp. pasta. Qu. L. pistus or Gr. πασσω, to sprinkle, or some root which signifies to mix and knead.} 1. A soft composition of substances, as flour moistened with water or milk and kneaded, or any kind of earth moistened and formed to the consistency of dough. Paste made of flour is used in cookery ; paste made of flour or earth, is used in various arts and manufactures, as cement.
VERMICELLI, n. {It. vermicello, a little worm, from vermis, a worm.} In cookery, little rolls or threads of paste, or a composition of flour, eggs, sugar and saffron ; used in soups and pottages.
An American Dictionary of the English Language (1847)—the first Merriam Brothers version of Webster's Dictionary exhibits a much clearer idea than its predecessors did of macaroni as pasta:
MACARONI, n. ... 1. Dough of whet flour made into a tubular or pipe form, of the thickness of a goose quill ; Italian or Genoese paste. ...
Paste, too, receives more detailed treatment in its relevant senses:
PASTE, n. ... 1. A soft composition of substances, as flour moistened with water or milk and kneaded, or any kind of earth moistened and formed into the consistence of dough, as in making potter's ware. 2. A kind of cement made of flour and water boiled, used for uniting paper or other substances
But noodle is still only a simpleton, vermicelli is still associated with "a composition of flour, eggs, sugar and saffron," and spaghetti is nowhere to be found.
The last of the three major editions of An American Dictionary of the English language (1864) is the first to define vermicelli in the pasta sense that people today are familiar with:
Vermicelli, n. ... The flour of a hard and small grained wheat made into dough, and forced through slender cylinders or pipes till it takes a slender, worm-like form, whence the Italian name.
Noodle finally makes the grade as a foodstuff in Webster's International Dictionary (1890):
Noodle, n. {G. nudel vermicelli.} A thin strip of dough, made with eggs, rolled up, cut into small pieces, and used in soup.
Spaghetti debuts in the same dictionary, with this entry:
Spaghetti n. {It.} A variety of macaroni made in tubes of small diameter.
And the entry for vermicelli, after repeating the definition from the 1864 An American Dictionary adds this note about how to distinguish between vermicelli and macaroni:
When the paste is made in larger tubes, it is called macaroni.
As of Webster's First Collegiate Dictionary (1898), this is where the relevant definitions stand:
Macaroni n. 1. Long slender tubes made of a paste chiefly of wheat flour, and used as food.
Noodle n. Dough, made with eggs, cut into small pieces, and used in soup.
Paste n. 1. A soft composition, as of moistened flour or earth. 2. Specif., in cookery, pastry dough.
Spaghetti, n. A variety of macaroni made in tubes of small diameter.
Vermicelli, n. Wheat flour made into a slender wormlike form : — whence the Italian name.
At least in the United States, macaroni, paste, and vermicelli appear in dictionaries in the context of food as far back as 1806. Noodle and spaghetti follow in 1890. But of the five words tracked in the Google Ngram above, none seems particularly negatively affected by the rise of pasta. Instead, their frequencies since 1970 seem to have risen slightly, though at a much less impressive trajectory than pasta has. And when you add paste (pink line) to the mix, just to see whether its frequency dropped as pasta's rose, you find that it rose too between 1970 and 2010:
So the rise of pasta seems, above all, to be due to an increase in interest in foods of the pasta group, not due to a zero-sum change in popularity of one term at the expense of another.
Still, you may wonder why English speakers jumped aboard the pasta train when they had a perfectly good English word (paste) that could be (and for many years had been) used to refer to the same generic category of starchy foods. One answer, surely, is that pasta arose not in the context of all noodle-like starches, but in the context of the specifically Italian subset of such starches—their abbondanza notwithstanding.
A second, more speculative answer relates to what I call "commercial correctness": companies are very keen not to have sales of their products hurt by issues of nomenclature. This is evident in such changes in food wordings as mahi-mahi (for dolphin [the fish, not the mammal], orange roughy (for slimehead), chevon (for goat meat), and canola oil (for rapeseed oil). It may be that purveyors of spaghetti- or macaroni-like foodstuffs felt that the generic term paste was sufficiently unappetizing to put a damper on public enthusiasm for the food category, whereas pasta sounded exotic, appealing, and unambiguously culinary.