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Abstract We present a sample of 34 normal Type II supernovae (SNe II) detected with the Zwicky Transient Facility, with multiband UV light curves starting att≤ 4 days after explosion, and X-ray observations. We characterize the early UV-optical color, provide empirical host-extinction corrections, and show that thet> 2 day UV-optical colors and the blackbody evolution of the sample are consistent with shock cooling (SC) regardless of the presence of “flash ionization” features. We present a framework for fitting SC models that can reproduce the parameters of a set of multigroup simulations up to 20% in radius and velocity. Observations of 15 SNe II are well fit by models with breakout radii <10¹⁴cm. Eighteen SNe are typically more luminous, with observations att≥ 1 day that are better fit by a model with a large >10¹⁴cm breakout radius. However, these fits predict an early rise during the first day that is too slow. We suggest that these large-breakout events are explosions of stars with an inflated envelope or with confined circumstellar material (CSM). Using the X-ray data, we derive constraints on the extended (∼10¹⁵cm) CSM density independent of spectral modeling and find that most SN II progenitors lose $\dot{M}<{10}^{-4}{M}_{\odot }{\mathrm{yr}}^{-1}$up to a few years before explosion. We show that the overall observed breakout radius distribution is skewed to higher radii due to a luminosity bias. We argue that the ${66}_{-22}^{+11}\%$of red supergiants (RSGs) explode as SNe II with breakout radii consistent with the observed distribution of RSGs, with a tail extending to large radii, likely due to the presence of CSM.