Here we explore the two-photon 6s[2 1]S0 → 6s23s [1]S0 transition in Yb as a two-photon clock, electrometer, or blackbody radiation (BBR) thermometer. The unique level structure of Yb places the 6s6p [1]P1 state s energy level at ≈ 49.7% of the ionization energy, which facilitates two-photon Doppler-free excitation of the 6s23s [1]S0 state from the ground 6s[2 1]S0 state at a relatively low optical intensity. This J = 0 → J = 0 transition is insensitive to first-order Zeeman and electric quadrupole shifts and is further predicted to have relatively low sensitivity to collisional effects. Using configuration interaction theory, we compute relevant properties of the 6s23s [1]S0 Rydberg state for sensing, including the C6 coefficient, dc polarizability, BBR shift, and BBR depopulation rates. As a first experimental step, we demonstrate Doppler-free spectroscopy of the 6s[2 1]S0 → 6s23s [1]S0 transition. From our Doppler-free spectroscopy, we estimate the natural linewidth (lifetime) of the 6s23s [1]S0 state to be 90 kHz (1.8 µs).