Please try the below.
If you want to change the default direction, change it on the ngOnInit method call to this.sortItem
// app.component.ts
import { Component, ViewChild } from '@angular/core';
import { Sort, MatSort, MatPaginator } from '@angular/material';
import { interval } from 'rxjs';
@Component({
  selector: 'my-app',
  templateUrl: './app.component.html',
  styleUrls: [ './app.component.css' ]
})
export class AppComponent  {
  public displayedColumns: string[] = ['name', 'break',];
  public sortedData: any;
  constructor( ) { }
  ngOnInit() {
    setTimeout(() => {         
      this.sortItem({ active: 'break', direction: 'asc' });
    }, 1000);
  }
  compare(a: number | string, b: number | string, isAsc: boolean) {
    return (a < b ? -1 : 1) * (isAsc ? 1 : -1);
  }
  sortItem(sort: Sort) {
    const data = DATA_SOURCE.slice();
    if (!sort.active || sort.direction === '') {
      this.sortedData = data;
      return;
    }
    this.sortedData = data.sort((a, b) => {
      const isAsc = sort.direction === 'asc';
      switch (sort.active) {
        case 'break': return this.compare(a.breakTime.start, b.breakTime.start, isAsc);        
        default: return 0;
      }
    });
  }
}
const DATA_SOURCE = [
  {
    name: 'Alice',
    breakTime: {
      start: '14-00',
      end: '14-00'
    },
  },
  {
    name: 'Steve',
    breakTime: {
      start: '10-00',
      end: '11-00'
    },
  },
  {
    name: 'Bob',
    breakTime: {
      start: '12-00',
      end: '13-00'
    },
  },
];
// app.component.html
<table mat-table [dataSource]="sortedData" multiTemplateDataRows 
       matSort (matSortChange)="sortItem($event)" 
       class="mat-elevation-z4 w-100">
  <ng-container matColumnDef="name">
    <th mat-header-cell *matHeaderCellDef> Name </th>
    <td mat-cell *matCellDef="let item"> {{item.name}} </td>
  </ng-container>
  <ng-container matColumnDef="break">
    <th mat-header-cell *matHeaderCellDef mat-sort-header > Break </th>
    <td mat-cell *matCellDef="let element">
      {{element.breakTime.start}} - {{element.breakTime.end}}
    </td>
  </ng-container>
  <tr mat-header-row *matHeaderRowDef="displayedColumns"></tr>
  <tr mat-row *matRowDef="let element; columns: displayedColumns;"
      class="element-row"
      [class.example-expanded-row]="expandedElement === element"
      (click)="expandedElement = expandedElement === element ? null : element">
  </tr>
</table>