We consider the classical evolution of the inflaton field and the Hubble parameter in homogeneous and isotropic single-field inflation models. Under an extremely broad assumption, we show that the Universe generically emerges from an initial singularity in a noninflating state where the kinetic energy of the inflaton dominates its potential energy. In this kinetically dominated regime, the dynamical equations admit simple analytic solutions are independent of the form the potential energy. In such models, these analytic solutions thus provide a simple way of setting the initial conditions from which to start the (usually numerical) integration of the coupled equations of motion. We illustrate this procedure by applying it to spatially flat models with polynomial and exponential potentials, and determine the background evolution in each case; generically the Hubble parameter and the inflation field as well as their time derivatives decrease during kinetic dominance until the onset of a brief period of fast-roll inflation prior to a slow-roll phase. We also calculate the approximate spectrum of scalar perturbations produced in each model and show that it exhibits a generic damping of power on large scales. This may be relevant to the apparent low-l falloff in the cosmic microwave background power spectrum.