This REALLY REALLY REALLY depends a) where you live and b) what you consider to be kosher.

If you are a Jew who follows kosher laws strictly, then in 2021 in most of the United States you still can't walk into a restaurant and order a kosher item off the menu.* So if it's alright with you, I'll reframe your question to be something like "how easily accessible is kosher food? If I find myself in a random town, will I be able to find food that I can eat for dinner?" (We're also going to assume that we're talking about Jews for whom it mattered to them if the food they were eating was kosher, which is not necessarily a sure thing.)

1876 is a really interesting year for you to pick- it's before the major influx of Russian Jewish immigrants that began in 1881, which made the American Jewish community even more New York-heavy than it already had been, but there had already been a large wave of Jewish immigration that had led to an already large Jewish community in New York as well as smaller but developing communities elsewhere in the country, mostly in large cities like Baltimore, Philadelphia, Chicago, etc but also in smaller cities and towns as Jews participated (on a small scale, but participated nonetheless) in the western expansion of the US. While there were small farming efforts at various points that were targeted at Jewish immigrants, they were generally doomed to failure- most Jews who lived outside of larger cities served as itinerant peddlers, sometimes settling in smaller towns and opening shops once they were settled.

As far as the availability of kosher food, a Jew in a large city with a Jewish community could generally find kosher food. Most Jewish communities had a kosher slaughterer (called a shochet) and kosher butcher, though in this era fraud was rampant in the kosher meat industry, whether you lived in New York or Oklahoma. Kosher meat is one of the most complex kosher foods to produce, in the sense that it requires the presence of Jews who are knowledgeable about the laws at basically every step of the way, and as a result it ends up being quite expensive. In the European Jewish communities from which many of these immigrants had come from, the production of kosher meat was overseen by the central rabbinate of the place where they lived, and this centralization had a government imprimatur. All of this was lacking in the US at this stage, and therefore the actual kosher status of purportedly kosher meat was often uncertain, as, in order to cut costs, a "kosher butcher" might, for example (and as actually happened), secretly sell non kosher cuts as kosher or add non-kosher meat to kosher meat when making sausages.

In addition, these large Jewish communities often had other kinds of kosher food available, whether through bakeries or appetizing shops or occasionally restaurants (though they weren't very common). At a time in which less food was processed and packaged, if one knew which ingredients were kosher, there were a lot of options. What made restaurants, in your original example, different was the fact that kosher laws include restrictions on cooking methods and dishes, mixing different ingredients, etc; but kosher food in and of itself for the average person's consumption was definitely available.

It got more complicated when you got to places which did not have Jewish communities. If you look at these traveling peddlers, for example, they often did feel the need to compromise on their level of observance of kosher laws while on the road (and often felt unease about it); while they could always eat things like fruit, vegetables, eggs, and milk, for many it would automatically be a problem if they ate anything cooked by their hosts on their own dishes, and yet at the end of a long day on the road they would have little choice. That said, those among whom they traveled, while often confused by these limitations, were often quite accommodating- some peddlers recorded that they had Christian hosts who would keep a special pot for them to cook their food, and the Cherokee tribe referred to Jewish peddlers as "egg eaters" because they would only eat hard-cooked eggs in the shell.

Peddlers often did their best to make it to a Jewish community for the weekend, so that at least on Shabbat they would be able to eat kosher food, attend synagogue, etc. Often they stayed at boardinghouses owned by Jewish women, who catered specifically to the traveling-peddler market in providing a warm environment with familiar kosher food from the old country. At a time when most Jewish immigrants to the US were male, looking to make their fortunes, this time in more established Jewish communities allowed them to meet local Jewish women, often leading them to settle down for themselves either in these established communities or by establishing their own- for example, in some small communities without a shochet or kosher butcher of their own, small groups of Jewish families might travel to a larger city every so often to buy large amounts of meat to store.

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*And here it gets way beyond the scope of a history sub and into an argument about what it means to follow kosher laws strictly and how this applies to eating in restaurants and such, so I'll leave it here.