Rydberg-atom electric field sensing has shown great potential from near-DC to THz with state-of-the-art measurement metrics realized in sensitivity, phase extraction, multi-band receptivity, etc. While Rydberg-atom sensors have shown exceptional performance in the GHz regime, low-frequency operation has remained challenging because of electric-field-screening in conventional vapor cells, which suppresses externally applied fields. We overcome this limitation by combining auxiliary modulation and lock-in detection with a paraffin-coated vapor cell, and demonstrate an electrode-free, wideband method for sensing frequencies, ranging from 0.5 Hz to 10 kHz. Our work extends Rydberg-atom sensor range to VLF, ULF, SLF, ELF and sub-ELF frequency bands. In our method, high state-of-the-art sensitivities have been achieved - 819 μV/cm/√Hz for 1 Hz, 33 μV/cm/√Hz for 10 Hz, 10 μV/cm/√Hz for 100 Hz and 2 μV/cm/√Hz for 1 kHz.