We compute an extensive set of early-time spectra of supernovae interacting with circumstellar material using the radiative transfer code CMFGEN. Our models are applicable to events observed from 1 to a few days after explosion. Using these models, we constrain the progenitor and explosion properties of a sample of 17 observed interacting supernovae at early-times. Because massive stars have strong mass loss, these spectra provide valuable information about supernova progenitors, such as mass-loss rates, wind velocities, and surface abundances. We show that these events span a wide range of explosion and progenitor properties, exhibiting supernova luminosities in the 1e8 to 1e12 Lsun range, temperatures from 10000 to 60000 K, progenitor mass-loss rates from a few 1e-4 up to 1 Msun/yr, wind velocities from 100 to 800 km/s, and surface abundances from solar-like to H-depleted. Our results suggest that many progenitors of supernovae interacting with circumstellar material have significantly increased mass-loss before explosion compared to what massive stars show during the rest of their lifetimes. We also infer a lack of correlation between surface abundances and mass-loss rates. This may point to the pre-explosion mass-loss mechanism being independent of stellar mass. We find that the majority of these events have CNO-processed surface abundances. In the single star scenario this points to a preference towards high-mass RSGs as progenitors of interacting SNe, while binary evolution could impact this conclusion. Our models are publicly available and readily applicable to analyze results from ongoing and future large scale surveys such as the Zwicky Transient Factory.
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