Geomagnetic indices derived from ground magnetic measurements characterize the intensity of solar-terrestrial interaction. The \textit{Kp} index derived from multiple magnetic observatories at mid-latitude has commonly been used for space weather operations. Yet, its temporal cadence is low and its intensity scale is crude. To derive a new generation of geomagnetic indices, it is desirable to establish a geomagnetic `baseline' that defines the quiet-level of activity without solar-driven perturbations. We present a new approach for deriving a baseline that represents the time-dependent quiet variations focusing on data from Chambon-la-Forêt, France. Using a filtering technique, the measurements are first decomposed into the above-diurnal variation and the sum of 24h, 12h, 8h, and 6h filters, called the daily variation. Using correlation tools and SHapley Additive exPlanations, we identify parameters that dominantly correlate with the daily variation. Here, we predict the daily `quiet' variation using a long short-term memory neural network trained using at least 11 years of data at 1h cadence. This predicted daily quiet variation is combined with linear extrapolation of the secular trend associated with the intrinsic geomagnetic variability, which dominates the above-diurnal variation, to yield a new geomagnetic baseline. Unlike the existing baselines, our baseline is insensitive to geomagnetic storms. It is thus suitable for defining geomagnetic indices that accurately reflect the intensity of solar-driven perturbations. Our methodology is quick to implement and scalable, making it suitable for real-time operation. Strategies for operational forecasting of our geomagnetic baseline 1 day and 27 days in advance are presented.