How to get the active tab In Angular Material2

Well, I'm not sure if I understood well your question because, by default the index always starts counting from zero unless you set manually the [selectedIndex] property.

Anyway, if you really want to see which tab is selected on initialization you could implement the AfterViewInit interface and do the following:

export class AppComponent implements AfterViewInit, OnInit {

...

  ngAfterViewInit() {
    console.log('afterViewInit => ', this.tabGroup.selectedIndex);
  }
}

On other hand, if you want to check which tab is selected based on changes (what makes more sense), here you go:

HTML:

<mat-tab-group #tabGroup (selectedTabChange)="tabChanged($event)">
  <mat-tab label="Tab 1">Content 1</mat-tab>
  <mat-tab label="Tab 2">Content 2</mat-tab>
</mat-tab-group>

Component:

tabChanged(tabChangeEvent: MatTabChangeEvent): void {
  console.log('tabChangeEvent => ', tabChangeEvent);
  console.log('index => ', tabChangeEvent.index);
}

DEMO

According to Material documentation Angular Material tabs output an event on tab change @Output() selectedTabChange: EventEmitter<MatTabChangeEvent>

Your Template:

<mat-tab-group (selectedTabChange)="tabChanged($event)">
  <mat-tab>
    <ng-template mat-tab-label>Tab 1</ng-template>
    Tab Content
  </mat-tab>
  <mat-tab>
    <ng-template mat-tab-label>Tab 2</ng-template>
    Tab Content
  </mat-tab>
</mat-tab-group>

Your Typescript:

import { MatTabChangeEvent } from '@angular/material';

public tabChanged(tabChangeEvent: MatTabChangeEvent): void {
    console.log(tabChangeEvent);
}