How to use the MatTableDataSource with an observable?

You should be able to new up the MatTableDataSource once at the class level and then use the data setter in ngOnInit.

dataSource = new MatTableDataSource<Thing>();
@ViewChild(MatPaginator, { static: true }) paginator: MatPaginator;
@ViewChild(MatSort, { static: true }) sort: MatSort;

ngOnInit() {
    getThings().subscribe(things => {
        this.dataSource.data = things;
        this.dataSource.paginator = this.paginator;
        this.dataSource.sort = this.sort;
    });
}