  In this article we develop a framework for studying parabolic semilinear
stochastic evolution equations (SEEs) with singularities in the initial
condition and singularities at the initial time of the time-dependent
coefficients of the considered SEE. We use this framework to establish
existence, uniqueness, and regularity results for mild solutions of parabolic
semilinear SEEs with singularities at the initial time. We also provide several
counterexample SEEs that illustrate the optimality of our results.
