Linear Stepper does not work with non-form content

You can try to use hidden checkboxes and mark them as checked when a certain condition is met. For example:

HTML:

<mdb-stepper #stepper [linear]="true">
    <mdb-step name="Step 1" [stepForm]="firstFormGroup">
      <form [formGroup]="firstFormGroup">
        <div class="md-form">
            <button type="button" mdbBtn color="primary" mdbWavesEffect (click)="completeFirst()">Complete first step</button>
            <mdb-checkbox hidden formControlName="first">First</mdb-checkbox>
        </div>
      </form>
      <button mdbBtn size="sm" color="primary" (click)="stepper.next()">CONTINUE</button>
    </mdb-step>
    <mdb-step name="Step 2" [stepForm]="secondFormGroup">
      <form [formGroup]="secondFormGroup">
        <div class="md-form">
            <button type="button" mdbBtn color="primary" mdbWavesEffect (click)="completeSecond()">Complete second step</button>
            <mdb-checkbox hidden formControlName="second">Second</mdb-checkbox>
        </div>
      </form>
      <button mdbBtn size="sm" color="primary" (click)="stepper.next()">CONTINUE</button>
      <button mdbBtn size="sm" color="secondary" (click)="stepper.previous()">BACK</button>
    </mdb-step>
    <mdb-step name="Step 3" label="Step 3 label">
      <p class="pl-2">Finish!</p>
      <div class="step-actions">
        <button mdbBtn  size="sm" color="primary" (click)="onSubmit()">SUBMIT</button>
      </div>
    </mdb-step>
  </mdb-stepper>

TS:

  firstFormGroup: FormGroup;
  secondFormGroup: FormGroup;

  ngOnInit() {
    this.firstFormGroup = new FormGroup({
      first: new FormControl(false, [Validators.requiredTrue])
    });
    this.secondFormGroup = new FormGroup({
      second: new FormControl(false, [Validators.requiredTrue])
    });
  }

  completeFirst() {
    this.first?.setValue(true);
  }

  completeSecond() {
    this.second?.setValue(true);
  }

  get first() { return this.firstFormGroup.get('first'); }
  get second() { return this.secondFormGroup.get('second'); }

  onSubmit() {
    // do something here
  }