We report direct evidence of conduction band filling in 3% La-doped BaSnO3 using hard x-ray photoelectron spectroscopy. Direct comparisons with hybrid density functional theory calculations support a 3.2 eV indirect band gap. The use of hybrid DFT is verified by excellent agreement between our photoelectron spectra and O K-edge x-ray emission and absorption spectra. Our experimental and computational results demonstrate that the conduction band is primarily of Sn 5s orbital character with little O 2p contribution, which is a prerequisite for designing a perovskite-based transparent conducting oxide.