By the early 19th century, smallpox vaccination was commonplace in Europe, though doctors were unaware of how it worked or how to extend the principle to other diseases. A transitional period began in the late 1850s with the work of Louis Pasteur. This work was later extended by Robert Koch in the 1880s. By the end of that decade, the miasma theory was struggling to compete with the germ theory of disease. Viruses were initially discovered in the 1890s. Eventually, a "golden era" of bacteriology ensued, during which the germ theory quickly led to the identification of the actual organisms that cause many diseases.

https://en.wikipedia.org/wiki/Germ_theory_of_disease

Looks like germ theory was around and starting to become accepted in the medical community, but it probably hadn't become widely known by the general population.