It looks like rather than having direct control over the page number, per se, you have control over the first row displayed:
<p-table [columns]="cols" [value]="cars" [paginator]="true" [rows]="10" [first]="first">
In the above case, with 10 rows per page, you'd set first
to 0 to get to the first page, 10 for the second page, 20 for the third page, etc.
Update:
Since the above didn't work for changing the page after the fact (perhaps it only works for the initial set-up of the table), you could try something like the following, which works for the now-deprecated DataTable:
In the HTML:
<p-table #myTable [columns]="cols" [value]="cars" [paginator]="true" [rows]="10">
Then, in your component:
@ViewChild('myTable') myTable: TurboTable;
...
this.myTable.first = desiredFirstRow;
I'll take this as an occasion to update my old table code to TurboTable, and I'll know soon enough if this works for sure.