  Many out of equilibrium phenomena, such as diffusion-limited reactions or
target search processes, are controlled by first-passage events. So far the
general determination of the mean first-passage time (FPT) to a target in
confinement has left aside aging processes, involved in contexts as varied as
glassy dynamics, tracer diffusion in biological membranes or transport of cold
atoms in optical lattices. Here we consider general non-Markovian
scale-invariant processes in arbitrary dimension, displaying aging, and
demonstrate that all the moments of the FPT obey universal scalings with the
confining volume with non trivial exponents. Our analysis shows that a
nonlinear scaling of the mean FPT with the volume is the hallmark of aging and
provides a general tool to quantify its impact on first-passage kinetics in
confinement.
