I doubt there is a standard time for these steps; it would depend on the recommendations of each equipment manufacturer. You are quite correct to seek this information; with luck it will be in the genset manual.
If the engine is equipped with a heated cooling water system, it will be ready to go and take load on short notice. Generally speaking, a few minutes each of warmup and cooldown is desirable. If possible add or drop loads sequentially rather than all at once.
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In vino veritas; in cervisia carmen; in aqua E. coli.