Using Parker Solar Probe observations, this Letter reports for the first time the existence of broadband electrostatic waves below the electron cyclotron frequency in the near-Sun solar wind and even in the extended solar corona. These waves have enhanced power spectral densities of the electric fields near the lower-hybrid frequency fLH, and their peak frequencies can be below or exceed fLH. The perturbed electric fields are distributed between about 0.1 and 50 mV m−1. Accompanying broadband electrostatic waves, strong electrostatic solitary structures can arise, and their peak amplitudes approach nearly 500 mV m−1. Due to the appearance of considerable electric field fluctuations perpendicular to the background magnetic field, the observed waves would propagate obliquely. Moreover, this Letter conjectures the wavenumber and frequency information for the candidate of the wave mode nature being the oblique slow mode wave, the ion Bernstein wave, or the oblique fast-magnetosonic whistler wave. One important consequence of the observed waves is that they may regulate the electron heat flux in the near-Sun solar wind and in the solar corona.