TYPESCRIPT

ion-datetime open programmatically

<ion-datetime #dateTime style="display:none" displayFormat="h:mm A" pickerFormat="h mm A" [(ngModel)]="startTime"></ion-datetime>
<button (click)="openStart()"></button>
and then in your code
...
//first create a reference to the datetime control:
@ViewChild('dateTime') sTime;
...
//then add your event code: 
openStart()
{
	this.sTime.open();
}