  Using magnetically trapped atomic hydrogen as an example, we investigate the
prospects of achieving Bose-Einstein condensation in a dilute Bose gas. We show
that, if the gas is quenched sufficiently far into the critical region of the
phase transition, the typical time scale for the nucleation of the condensate
density is short and of $O(\hbar/k_{B}T_{c})$. As a result we find that
thermalizing elastic collisions act as a bottleneck for the formation of the
condensate. In the case of doubly-polarized atomic hydrogen these occur much
more frequently than the inelastic collisions leading to decay and we are lead
to the conclusion that Bose-Einstein condensation can indeed be achieved within
the lifetime of the gas.
