We experimentally demonstrate a digital-to-analog-converter-less (DAC-less) vestigial sideband (VSB) 4-level pulse amplitude modulation (PAM4) transmission system for data center interconnects (DCIs) using a silicon photonic (SiP) multi-electrode Mach-Zehnder modulator (ME-MZM) based DAC-less transmitter and a VSB self-coherent receiver. The impacts of linear and nonlinear impairments on the proposed system and their mitigation methods are comprehensively studied. By using Kramer-Kronig (KK) detection, frequency domain chromatic dispersion compensation, and short-memory time domain Volterra equalization at the receiver, we report a 112 Gb/s PAM4 transmission over 40 km standard single mode fiber (SSMF) with a bit error rate (BER) below the 7% overhead (OH) hard-decision forward error correction threshold of 3.8 × 10-3, and a 120 Gb/s PAM4 transmission over 80 km SSMF with a BER below the 20% OH soft-decision forward error correction threshold of 2 × 10-2, without any transmitter side digital signal processing such as pre-emphasis and pulse shaping.