We report on a cooperative phenomenon of ferromagnetism and unconventional superconductivity (SC) in UGe$_2$ through the measurements of $^{73}$Ge nuclear-quadrupole-resonance (NQR) under pressure ($P$). The NQR spectra evidenced phase separation into ferromagnetic and paramagnetic phases in the vicinity of $P_csim 1.5$ GPa, pointing to a first-order transition. The measurements of nuclear-spin-lattice-relaxation-rate $1/T_1$ revealed that SC emerges under the background of ferromagnetism, but not of the paramagnetic phase.