Kinetic instabilities arising from anisotropic electron velocity distributions are ubiquitous in ionospheric, cosmic, and terrestrial plasmas, yet there are only a handful of experiments that purport to validate their theory. It is known that optical field ionization of atoms using ultrashort laser pulses can generate plasmas with known anisotropic electron velocity distributions. Here, we show that following the ionization but before collisions thermalize the electrons, the plasma undergoes two-stream, filamentation, and Weibel instabilities that isotropize the electron distributions. The polarization-dependent frequency and growth rates of these kinetic instabilities, measured using Thomson scattering of a probe laser, agree well with the kinetic theory and simulations. Thus, we have demonstrated an easily deployable laboratory platform for studying kinetic instabilities in plasmas.