What is the usage of のには? I think that「の」means「こと」, that is, a generic event. But I can't understand the usage of には in this case.
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の as you said is the nominalizer. You could have used こと instead.
びっくりする means "to be surprised". には are just the normal particles, and would be translated by "at" here.
彼女が最初に来たのにはびっくりした。 : I got surprised at the fact she came in first.
The は indicates a contrast, and you could have omitted it. The に is the same に you would use for other expressions like に驚く.
In the dictionary, you can see the exact definition for this usage:
(or at least I think this is the one)