I figured it out. These two attributes should be added:
sortField="userName" [sortOrder]="-1"
The sortField matches the column name and the sortOrder can be either 1 for ascending and -1 for descending.
Here’s the working solution:
<p-dataTable [value]="webUserSummaryList" [rows]="10" reorderableColumns="true" sortField="userName" sortOrder="-1">
<p-column field="userName" header="Username" [filter]="true" [sortable]="true"></p-column>
<p-column field="emailAddress" header="Email" [filter]="true" [sortable]="true"></p-column>
<p-column field="firstName" header="First Name" [filter]="true" [sortable]="true"></p-column>
<p-column field="lastName" header="Last Name" [filter]="true" filterMatchMode="contains" [sortable]="true"></p-column>