Generation and manipulation of coherent acoustic phonons enables ultrafast control of solids and has been exploited for applications in various acoustic devices. We show that localized coherent acoustic phonon wave packets can be launched by ultrafast Coulomb forces in a scanning tunneling microscope (STM) using tip-enhanced terahertz electric fields. The wave packets propagate at the speed of the longitudinal acoustic phonon, creating standing waves up to 0.26 THz for a 6.4 nm thin Au film on mica. The ultrafast lattice displacement can be as large as 5 pm and is precisely controlled by varying the tip-sample distance. This nonthermal femtosecond Coulomb-force-based excitation mechanism is applicable in nano-optomechanics for advanced terahertz engineering and opens new perspectives in exploiting coherent phonons at the atomic scale.