When Coulomb began his research into electric force (which would become known as Coulomb's law), Newton's law of universal gravitation had already discovered. As it would turn out electrical forces would parallel Newton's discovery in many ways. With both Coulomb's law and Newton's law of universal gravitation being proportional to inverse squared relationships.
Coulomb's work would become one of the first cases where electric charge was measured quantitatively. In the 1740's electricity was beginning to become well know. By the 1750's, Benjamin Franklin's had shown that lightning was an electrical phenomenon thereby proving that that electricity did exist in nature. Franklin's work became an inspiration to others and spawned research into the study of electricity and measurement of it.
Instruments which could indicate electricity had existed since the 1730's, however these tools did not approach real qualitative measurements. John Canton introduced an improved electrical indicator in 1753. Others such as Tiberius Cavallo of Italy concentrated their efforts atmospheric electricity, producing tools which could indicate the presence of electricity, but were a long way from quantitative measurements.