Sound field estimation methods based on kernel ridge regression have proven effective, allowing for strict enforcement of physical properties, in addition to the inclusion of prior knowledge such as directionality of the sound field. These methods have been formulated for single-frequency sound fields, restricting the types of data and prior knowledge that can be used. In this paper, the kernel ridge regression approach is generalized to consider discrete-time sound fields. The proposed method provides time-domain sound field estimates that can be computed in closed form, are guaranteed to be physically realizable, and for which time-domain properties of the sound fields can be exploited to improve estimation performance. Exploiting prior information on the time-domain behaviour of room impulse responses, the estimation performance of the proposed method is shown to be improved using a time-domain data weighting, demonstrating the usefulness of the proposed approach. It is further shown using both simulated and real data that the time-domain data weighting can be combined with a directional weighting, exploiting prior knowledge of both spatial and temporal properties of the room impulse responses. The theoretical framework of the proposed method enables solving a broader class of sound field estimation problems using kernel ridge regression where it would be required to consider the time-domain response rather than the frequency-domain response of each frequency separately.