You can use appearance=”outline”. The datepicker icon is in the inner of the mat-form-field border.
Try this:
<mat-form-field appearance="outline">
<mat-label>Outline form field</mat-label>
<input matInput placeholder="Placeholder" [matDatepicker]="myDatepicker">
<mat-datepicker-toggle matSuffix [for]="myDatepicker"></mat-datepicker-toggle>
<mat-datepicker #myDatepicker></mat-datepicker>
<mat-hint>Hint</mat-hint>
</mat-form-field>
See: stackblitz