Open the datepicker calendar without showing the edittextbox in xamarin.forms

Make the DatePicker control hidden by setting IsVisible=false. Then you can trigger it programmatically by calling the Focus() method from elsewhere in your code.

Check this :

        DatePicker datePicker = new DatePicker
        {
            Format = "D",
            VerticalOptions = LayoutOptions.CenterAndExpand,
            IsVisible =false,
            IsEnabled = false
        };

        Button button = new Button
        {
            Text = "Date",
            VerticalOptions = LayoutOptions.CenterAndExpand
        };
        button.Clicked += (object sender, EventArgs e) =>
        {
            IsEnabled = true;
            datePicker.Focus();
            button.Text = datePicker.Date.ToString();
        };

Refer : https://developer.xamarin.com/api/type/Xamarin.Forms.DatePicker/