It is not a verb. Here is the original sentence:
Frauen verbringen im Durchschnitt 76 Tage ihres Lebens mit dem Wühlen in der Handtasche.
-Women spend in average 76 days of their life with --- in the handbag.
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It is very common in German to convert verbs to nouns. There are several ways of doing so one of them is using the inifinitve form, capitalize the verb, and give it a neuter grammatical gender:
wühlen - das Wühlen
Thererefore whenever you find a noun not listed in a dictionary you may still find the verb it was derived from.