It won't take more than a minute.
No more than a minute. It won't be bright all the time, but it will glow instantly. The magnet must produce a sufficiently rapid shuttling motion in the coil, or a sufficiently rapid reciprocating motion. As long as the induced current generated by the magnet's magnetic field lines cut by the coil reaches the bottom line of the bulb, the bulb. will light up.
In the future, as technology becomes more advanced and materials improve, or more materials are added, the lighting duration may be longer.