Virtual reality (VR) presents immersive opportunities across many applications, yet the inherent risk of developing cybersickness during interaction can severely reduce enjoyment and platform adoption. Cybersickness is marked by symptoms such as dizziness and nausea, which previous work primarily assessed via subjective post-immersion questionnaires and motion-restricted controlled setups. In this paper, we investigate the dynamic nature of cybersickness while users experience and freely interact in VR. We propose a novel method to continuously identify and quantitatively gauge cybersickness levels from users' passively monitored electroencephalography (EEG) and head motion signals. Our method estimates multitaper spectrums from EEG, integrating specialized EEG processing techniques to counter motion artifacts, and, thus, tracks cybersickness levels in real-time. Unlike previous approaches, our method requires no user-specific calibration or personalization for detecting cybersickness. Our work addresses the considerable challenge of reproducibility and subjectivity in cybersickness research. In addition to our method's implementation, we release our dataset of 16 participants and approximately 2 hours of total recordings to spur future work in this domain. Source code: https://github.com/eth-siplab/EEG_Cybersickness_Estimation_VR-Beyond_Subjectivity.