As noted in @Conifold's comment, identifying the first popular science book is an impossible task. Before the specialization of science that accelerated during the 19th century, there was often little distinction between "science" and "popular science" for the small part of the population that was educated and literate.
Books that have been called the "first popular science book" include:
Another interesting example of Enlightenment popular science is Erasmus Darwin's "The Botanic Garden" published in 1791. According to wikipedia:
The intent of The Botanic Garden, one of the first popular science books, is to pique readers' interest in science while educating them at the same time.
The format of this book is unusual for modern readers since it is the form of two long poems: "The Loves of the Plants" and "The Economy of Vegetation". Explaining science in to the educated populace in poetic form actually has a long history, and contributors to the 2018 conference "Genealogy of Popular Science
From Ancient Ecphrasis to Virtual Reality" argued that European science popularization goes back to the didactic poetry of Greek and Roman antiquity.
As noted in other answers and comments, another "popular science" genre from antiquity through the 18th Century were handbooks intended to share practical scientific and technical knowledge. As described by Stahl in "Roman science: origins, development, and influence to the later Middle Ages"
Most [ancient Greek and Roman] handbooks were intended for the general reader. Such books were occasionally written by men who had made original contributions to Greek scientific thought; more often the authors themselves had limited competence in handling scientific subjects or were laymen used to presenting any subject in a simplified form.
Without these popular works, much of the scientific knowlege of the era might have been lost. For example, all the original works of the 4th century BCE Greek astronomer Eudoxus have been lost, but his contributions were largely preserved in the didactic poem "Phenomena" written a century later.
This "handbook" tradition continued right through to the invention of the printing press, and later examples include books of secrets such as Giambattista Della Porta's 1558 Magia Naturalis and Isabella Cortese's 1561 "I secreti della signora Isabella Cortese".