High-gain optical parametric amplification is an important nonlinear process used both as a source of coherent infrared light and as a source of nonclassical light. In this work, we experimentally demonstrate an approach to optical parametric amplification that enables extremely large parametric gains with low energy requirements. In conventional nonlinear media driven by femtosecond pulses, multiple dispersion orders limit the effective interaction length available for parametric amplification. Here, we use the dispersion engineering available in periodically poled thin-film lithium niobate nanowaveguides to eliminate several dispersion orders at once. The result is a quasi-static process; the large peak intensity associated with a short pump pulse can provide gain to signal photons without undergoing pulse distortion or temporal walk-off. We characterize the parametric gain available in these waveguides using optical parametric generation, where vacuum fluctuations are amplified to macroscopic intensities. In the unsaturated regime, we observe parametric gains as large as 71 dB (118 dB/cm) spanning 1700–2700 nm with pump energies of only 4 pJ. When driven with pulse energies > 10 p J , we observe saturated parametric gains as large as 88 dB ( > 146 d B / c m ). The devices shown here achieve saturated optical parametric generation with orders of magnitude less pulse energy than previous techniques.