Eighteenth-century Americans would have known very little about Buddhism, Hinduism, Sikhism or any other Asian religion tradition. Awareness of Asian religions really only took off in the mid-nineteenth century.
What Did People Know?
Most commentators in both the US and Europe in the eighteenth century divided religion into Christian, Jewish, Muslim, and "pagan" categories. Asian religious traditions were lumped into this "heathen" or "pagan" category. Even people on what might be described as the religious left, like Thomas Jefferson, typically divided the world this way.
The first printed description of Hinduism in English-speaking North America was from Hannah Adams, a Massachusetts writer, in her 1784 book An Alphabetical Compendium of the Various Sects Which Have Appeared in the World from the Beginning of the Christian Era to the Present Day. It's one of the first texts on comparative religion, though it had a strong Unitarian Christian perspective.
Mentions of Hinduism
Adams outlined the belief of "Gentoos" (as she called them), saying they had a lawgiver called Brahma and taught belief in a supreme being. She accused Brahmin priests of abandoning monotheism to embrace polytheism. The depiction of pure monotheistic religion being destroyed by priests was a common trope among Unitarians, English deists, and American religious skeptics.
Adams's book went through several editions under the title Dictionary of All Religions in the early nineteenth century. She also expanded the coverage of Hinduism with new material arriving from Europe. There was even a very short paragraph on Buddhism that referred readers to the entry on Hinduism. Though it sold well, it was a specialized text, and Hinduism was only one entry in the massive tome, so it seems unlikely even most educated people would have known much about it.
The controversial English Unitarian Joseph Priestly, who immigrated to the United States and befriended Thomas Jefferson, wrote a comparative religious text, A Comparison of the Institutes of Moses with those of the Hindoo and Other Ancient Nations, in 1799. This argued against a theory put forward by French writer Louis-Mathieu Langlès, that the Vedas had inspired the Pentateuch, and claimed the Hebrew Scriptures were superior to the Vedas. The book does not seem to have been widely read in the United States, though.
When Did People Learn About Asian Religions?
By the middle of the nineteenth century there began to be an interest in Asian religions, aided in part by texts coming from England about India. There was also a growing European scholarship on Buddhism that was arriving the United States.
The first academic expert in Asian religions in the U.S. was Edward Elbridge Salisbury, a minister who taught Arabic and Sanskrit at Yale from 1841 to 1854. He was also one of the founders of the American Oriental Society, which studied Asian religions, among other topics.
The Transcendentalist movement in particular embraced the study of these new religious ideas. Henry David Thoreau, for example, translated parts of the work of French scholar of Buddhism Eugène Burnouf and published them in the Transcendentalist periodical The Dial, making parts of the Lotus Sutra available in English. Ralph Waldo Emerson wrote poetry invoking Hindu ideas, his poem "Brahma" perhaps being the most famous.
Works Referenced:
Altman, Michael J. Heathen, Hindoo, Hindu: American Representations of India, 1721-1893. New York: Oxford University Press, 2017.
Tweed, Thomas A. The American Encounter with Buddhism, 1844-1912: Victorian Culture and the Limits of Dissent. Chapel Hill, NC: The University of North Carolina Press, 1992.