Abstract We present early results from the Epoch of Giant Planet Migration program, a precise radial velocity (RV) survey of more than 100 intermediate-age (∼20–200 Myr) G and K dwarfs with the Habitable Zone Planet Finder spectrograph (HPF) at McDonald Observatory’s Hobby–Eberly Telescope. The goals of this program are to determine the timescale and dominant physical mechanism of giant planet migration interior to the water ice line of Sun-like stars. Here, we summarize results from the first 14 months of this program, with a focus on our custom RV pipeline for HPF, a measurement of the intrinsic near-infrared RV activity of young Solar analogs, and modeling the underlying population-level distribution of stellar jitter. We demonstrate on-sky stability at the sub-2 m s⁻¹ level for the K2 standard HD 3765 using a least-squares matching method to extract precise RVs. Based on a subsample of 29 stars with at least three RV measurements from our program, we find a median rms level of 34 m s⁻¹. This is nearly a factor of 2 lower than the median rms level in the optical of 60 m s⁻¹ for a comparison sample with similar ages and spectral types as our targets. The observed near-infrared jitter measurements for this subsample are well reproduced with a log-normal parent distribution with μ = 4.15 and σ = 1.02. Finally, by compiling rms values from previous planet search programs, we show that near-infrared jitter for G and K dwarfs generally decays with age in a similar fashion to optical wavelengths, albeit with a shallower slope and lower overall values for ages ≲1 Gyr.