The magnetic fields of the quiet Sun cover at any time more than 90% of its surface and their magnetic energy budget is crucial to explain the thermal structure of the solar atmosphere. One of the possible origins of these fields is the action of the local dynamo in the upper convection zone of the Sun. Existing simulations of the local solar dynamo require an initial seed field and sufficiently high spatial resolution in order to achieve the amplification of the seed field to the observed values in the quiet Sun. Here we report an alternative model of seeding based on the action of the Bierman battery effect. This effect generates a magnetic field due to the local imbalances in electron pressure in the partially ionized solar plasma. We show that the battery effect self-consistently creates from zero an initial seed field of a strength of the order of micro G, and together with dynamo amplification allows the generation of quiet Sun magnetic fields of a similar strength to those from solar observations.