How to show current month on button click?

I Want to show the current month according to the system time date. Week and Date is working accordingly system date.

It looks like you are missing "configMonth" change in your method:

currentDate(date: DayPilot.Date): void {
  this.configDay.startDate = date;
  this.configWeek.startDate = date;
  this.configMonth.startDate = date;
  let dt = new DayPilot.Date(this.configWeek.startDate || this.configDay.startDate || this.configMonth.startDate);
  this.dateString = dt.toString("MMMM d, yyyy")
}

Sorry about that. I already used this but forget to mention it in the code. When I used this I get an error like
"this.startDate.firstDayOfMonth is not a function " in console.

this is my code for the month on function changeDate()

let dt = new DayPilot.Date(this.configMonth.startDate).addMonths(value * 1).firstDayOfMonth();

let day = dt.toString("dddd");
if (day == "Saturday") {
dt = dt.addDays(value > 0 ? value * 2 : value * 1);
} else if (day == "Sunday") {
dt = dt.addDays(value > 0 ? value * 1 : value * 2);
}