Observing and characterizing young planetary systems can aid in unveiling the evolutionary mechanisms that sculpt the mature exoplanet population. As an all-sky survey, NASA's Transiting Exoplanet Survey Satellite (TESS) has expanded the known young planet population as it has observed young comoving stellar populations. This work presents the discovery of a multiplanet system orbiting the 61$\pm 6$ Myr old G4V star TIC 434398831 ($M_\star = 0.99\, \mathrm{M_\odot }$, $R_\star = 0.91\, \mathrm{R_\odot }$, $T_\mathrm{eff} = 5638\,$K, $T\mathrm{mag} = 11.31$) located in the Theia 116 comoving population. We estimate the population's age based on rotation periods measured from the TESS light curves, isochrone fitting, and measurements of lithium equivalent widths in the spectra of Theia 116 members. The TESS FFI light curves reveal a mini-Neptune ($R_b = 3.51\, \mathrm{R_{\oplus }}$, $P_b = 3.69$ d) and super-Neptune ($R_c = 5.63\, \mathrm{R_{\oplus }}$, $P_c = 6.21$ d) with an orbital period ratio slightly larger than 5:3. Follow-up observations from CHEOPS and ground-based telescopes confirm the transits of TIC 434398831 b and c, and constrain their transit times. We explore the potential mass-loss histories of the two planets in order to probe possible initial conditions of the planets immediately after formation.