Given that mumps can be spread before symptoms appear, the incubation time is usually 16 to 18 days (range: 12 to 25 days), and four year old girls aren't very likely to be able to describe a situation where they might have been exposed, the index case had plenty of chances to catch it. It could have been in a store, where she touched something that had been touched by a transient traveler who stopped in the store earlier.
On average, the mumps vaccine is 88% effective after two doses. However, it is only 78% effective after one dose. Children are not given a second dose until between ages 4 and 6. Thus, on average, 22% of the children at the day care would have been susceptible. But, probability being what it is, more or fewer children could have caught the disease without that being any indicator of some alteration in the virus.
According to the CDC, there was an outbreak in Iowa in 2015-16, in which over a hundred college students came down with mumps. Perhaps one of those students stopped in your town before becoming symptomatic.
It would be interesting to see a phylogenetic analysis of the virus from the outbreak in your town and the college outbreak. Actually, those analyses can give a very detailed picture of the spread of the virus between communities, even if the actual person who transmitted the virus cannot be located.
If I remember right, the outbreak was prior to the college one. It was 2013/14 time frame. I do remember the college outbreak, and there was some speculation that it came from the same strain that hit western Scott county earlier.