We report Raman sideband cooling beyond the so-called Lamb-Dicke regime where all previous work lies. Our techniques open a route to ground-state cooling of systems such as light atoms and laser-cooled polar molecules where high trapping frequency and low initial thermal occupation are so far hard to achieve. Ground-state cooling in those systems are important to realize long coherence time in future quantum applications. Our specific demonstration using single sodium atoms allows such a system to serve as an interesting source for quantum assembling of complex system, such as ultracold polar molecules or coherent atom arrays.