We present the first results from the GeMS/GSAOI Galactic Globular Cluster Survey (G4CS) of the Milky Way globular clusters NGC 3201 and NGC 2298. Using the Gemini South Adaptive Optics Imager (GSAOI), in tandem with the Gemini Multi-conjugate adaptive optics System (GeMS) on the 8.1 m Gemini-South telescope, we collected deep near-IR observations of both clusters, resolving their constituent stellar populations down to K s ≃ 21 Vega mag. Point-spread function (PSF) photometry was performed on the data using spatially variable PSFs to generate JHK s photometric catalogs for both clusters. These catalogs were combined with Hubble Space Telescope (HST) data to augment the photometric wavelength coverage, yielding catalogs that span the near-UV to near-IR. We then applied 0.14 mas yr‑1 accurate proper-motion cleaning and differential-reddening corrections and chose to anchor our isochrones using the lower main-sequence knee and the main-sequence turnoff prior to age determination. As a result of the data quality, we found that the K s versus F606W ‑ K s and F336W versus F336W ‑ K s color–magnitude diagrams were the most diagnostically powerful. We used these two color combinations to derive the stellar population ages, distances, and reddening values for both clusters. Following isochrone fitting using three different isochrone sets, we derived best-fit absolute ages of 12.2 ± 0.5 Gyr and 13.2 ± 0.4 Gyr for NGC 3201 and NGC 2298, respectively. This was done using a weighted average over the two aforementioned color combinations, following a pseudo-χ 2 determination of the best-fit isochrone set. Our derived parameters are in good agreement with recent age determinations of the two clusters, with our constraints on the ages being or ranking among the most statistically robust.