We report on the dynamics of optically induced nuclear spin polarization in individual CdTe/ZnTe quantum dots loaded with one electron by modulation doping. The fine structure of the hot trion (charged exciton $X^-$ with an electron in the $P$-shell) is identified in photoluminescence excitation spectra. A negative polarisation rate of the photoluminescence, optical pumping of the resident electron and the built-up of dynamic nuclear spin polarisation (DNSP) are observed in time-resolved optical pumping experiments when the quantum dot is excited at higher energy than the hot trion triplet state. The time and magnetic field dependence of the polarisation rate of the $X^-$ emission allows to probe the dynamics of formation of the DNSP in the optical pumping regime. We demonstrate using time-resolved measurements that the creation of a DNSP at B=0T efficiently prevents longitudinal spin relaxation of the electron caused by fluctuations of the nuclear spin bath. The DNSP is built in the microsecond range at high excitation intensity. A relaxation time of the DNSP in about 10 microseconds is observed at $B=0T$ and significantly increases under a magnetic field of a few milli-Tesla. We discuss mechanisms responsible for the fast initialisation and relaxation of the diluted nuclear spins in this system.
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