We present a real-time method based on the propagation of the time-dependent Schrödinger equation in the space of electronic states to compute near edge x-ray absorption fine structure (NEXAFS) spectra of molecules from the ground or a valence excited state. Transition dipole moments between a core and a valence state are computed from linear-response time-dependent density functional theory implemented in the Amsterdam Modeling Suite package by using Slater-Condon rules following two distinct core and valence excited-state calculations. The implementation is compatible with any singly excited ansatz and generalizable to correlated wavefunction methods. The method has been applied to the ultrafast internal conversion observed in the gas-phase thymine, when excited to bright ππ* (S2) state. We have computed the NEXAFS O K-edge from the electronic ground state, S2, and the dark nπ* (S1) state. We have reproduced the experimental spectrum [Wolf et al., Nat. Commun. 8, 29 (2017)] after the pump, showing the peak at 526.5 eV associated with S1. The stochastic Schrödinger equation has been used to get a time-resolved NEXAFS signal, introducing the experimental S2 → S1 decay time of 60 fs. An implicit pump initializes the thymine in the S2 state, and an x-ray pulse probes the system at various delay times (and distinct thymine structures), leading to a time-resolved spectral profile that captures the S2 → S1 population transfer. Slower relaxation from S1 to the ground state has been also considered in a multiple-channel modeling of the dynamics. Ground- and excited-state NEXAFS spectra of cis and trans isomers of azobenzene have been also computed.