Global warming is making extreme wave events more intense and frequent. Hence, the importance of monitoring the sea state for marine risk assessment and mitigation is increasing day-by-day. In this work, we exploit the ubiquitous seismic noise generated by energy transfer from the ocean to the solid earth (called microseisms) to infer the sea wave height data provided by hindcast maps. To this aim, we use a combined approach based on statistical analysis and machine learning. In particular, a random forest model shows very promising results in the spatial and temporal reconstruction of sea wave height by microseisms. The observed dependence of input importance from the distance sea grid cell-seismic station suggests how the reliable monitoring of the sea state in a wide area by microseisms needs data recorded by dense networks, comprising stations evenly distributed along the coastlines.