Sophie Germain was born in Paris at a house on rue Saint-Denis—the birth certificate does not provide a number — on April 1, 1776, the daughter of Ambroise-François Germain and Marie-Madeleine Gruguelu. According to H. Stupuy, her first biographer on record, Sophie's father was a wealthy silk merchant (Marchand de soie en bottes) with a recorded address of rue St- Denis, No. 336. This house was at the level of la Fontaine des SS. Innocents (Fountain of the Innocents).

Very little is known about Sophie's childhood, but historians define the start of the French Revolution as the time of her mathematical awakening. Germain was born during the kingdomof the tragically infamous Louis XVI and Marie-Antoinette, and she came of age during a time of social strife in Paris in those tumultuous years of insurrection against the monarchy. This was also an era of mathematical revolution. France at that time made an enormous contribution to the fund of mathematical knowledge, including the development of modern analysis and mathematical physics.

When Sophie was a teenager, seven of the greatest mathematicians of the eighteenth century worked in the French Academy of Sciences, located not far from her home: Joseph-Louis Lagrange (1736–1813), Marie Jean Antoine Nicolas de Caritat, Marquis de Condorcet (1743–1794), Gaspard Monge (1746–1818), Pierre-Simon Laplace (1749–1827), Adrian-Marie Legendre (1752–1833), Jean Baptiste Joseph Fourier (1768–1830), and Siméon Denis Poisson (1781–1840).