  We consider the first-passage problem for $N$ identical independent particles
that are initially released uniformly in a finite domain $\Omega$ and then
diffuse toward a reactive area $\Gamma$, which can be part of the outer
boundary of $\Omega$ or a reaction centre in the interior of $\Omega$. For both
cases of perfect and partial reactions, we obtain the explicit formulas for the
first two moments of the fastest first-passage time (fFPT), i.e., the time when
the first out of the $N$ particles reacts with $\Gamma$. Moreover, we
investigate the full probability density of the fFPT. We discuss a significant
role of the initial condition in the scaling of the average fastest
first-passage time with the particle number $N$, namely, a much stronger
dependence ($1/N$ and $1/N^2$ for partially and perfectly reactive targets,
respectively), in contrast to the well known inverse-logarithmic behaviour
found when all particles are released from the same fixed point. We combine
analytic solutions with scaling arguments and stochastic simulations to
rationalise our results, which open new perspectives for studying the relevance
of multiple searchers in various situations of molecular reactions, in
particular, in living cells.
