For example, is this sentence correct?
The requested goods must be delivered within 5 business days upon receipt of a request (or simply upon request).
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It is acceptable to say upon; of or from would be better.
The normal pattern is:
To understand why upon is also acceptable, notice that we can also just say:
When the of / from part of the structure is missing, the [event] must be inferred from context. We can make that context explicit by adding an upon modifier to the beginning sentence:
Or we can add it to the end of the sentence:
So, to reiterate, within ... upon ... is acceptable, but within ... of ... and within ... from ... are preferable.