In this letter we present the first measurements of an exclusive electron
neutrino cross section with the MicroBooNE experiment using data from the
Booster Neutrino Beamline at Fermilab. These measurements are made for a
selection of charged-current electron neutrinos without final-state pions.
Differential cross sections are extracted in energy and angle with respect to
the beam for the electron and the leading proton. The differential cross
section as a function of proton energy is measured using events with protons
both above and below the visibility threshold. This is done by including a
separate selection of electron neutrino events without reconstructed proton
candidates in addition to those with proton candidates. Results are compared to
the predictions from several modern generators, and we find the data agrees
well with these models. The data shows best agreement, as quantified by
p-value, with the generators that predict a lower overall cross section, such
as GENIE v3 and NuWro