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Do you mean the rise time of the oscillation or the start-up time for the crystal once power has been applied to the PCB.
If rise time of the oscillation you should capture the crystal sine wave and measure the 10% - 90% time.
If start up time you will have to capture the point that the VCC supply to the relevant IC goes high (say 3v for a 3.3v part) and also capture the 1st oscillation of the crystal and then simply measure the time between the two.
Generally crystal outputs are of low amplitude sine waves and it is difficult to measure the rise time. If rise time matters most, better to use SMD oscillators in place of crystals and the data sheet of oscillators mention about the rise time.
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