Like many families with young children, Stan and Julia Usherenko had long planned to move to the suburbs, where they could afford a larger home and a yard. This year, they finally started what they assumed would be a leisurely search. Then the pandemic hit.

In mid-March—the last weekend that real-estate agents could hold an open house—Mr. and Mrs. Usherenko rushed to make an offer on a three-bedroom house in Midland Park, N.J., with a pool and fenced-in yard.

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