U can set the Input or Input with type="date" (datetimepicker) using JQuery.
In Razor view
@Html.TextBoxFor(m => m.StartedDate, new { @id = "mydate", @type = "date", @class = "form-control" })
Here is the JS code
$(document).ready(function () {
var dateNewFormat, onlyDate, today = new Date();
dateNewFormat = today.getFullYear() + '-'';
if (today.getMonth().length == 2) {
dateNewFormat += (today.getMonth() + 1);
}
else {
dateNewFormat += '0' + (today.getMonth() + 1);
}
onlyDate = today.getDate();
if (onlyDate.toString().length == 2) {
dateNewFormat += '"-'" + onlyDate;
}
else {
dateNewFormat += '-0' + onlyDate;
}
$('#mydate').val(dateNewFormat);
});