In USA, is there a particular date in a month, on which if I pay off the total balance for credit cards, so that my credit score can get increased?

First off, while it is true that the balance your credit card company reports does have an impact on your credit score, it is unlikely that changing when you make your payment is going to have a meaningful impact on your credit score. If you're paying your balance off every month, it is unlikely that your credit utilization is particularly high and likely that it is pretty constant because most people spend roughly the same amount every month. The difference between a credit card being reported with a $0 balance and one being reported with a month of spending is unlikely to amount to more than a handful of points. Since credit decisions are based on which of several rather wide buckets-- banks may offer one rate to everyone with a score of 740+, a different rate to those 670-739, etc-- changes of a handful of points are going to have exactly 0 impact on the terms on which most people are offered credit.

Your credit card company reports data to the credit bureaus monthly. Each company is free to decide what day to use for that reporting. You can look to see when each of the companies you have credit cards with report by seeing what balance was reported and working back to what day that would reflect. My experience is that most companies choose to report data as of the statement date or the end of the month but your mileage may vary (particularly if you choose your own statement date). If you figure out when each of your credit cards report, you can work back to figure out when you need to make a payment to reduce the balance that is reported.

Credit score in the U.S. is based on the information in your credit report. One of the factors of your credit score is credit utilization, which is a function of your credit card balances and your available credit. These balances are reported monthly to your credit report by your credit card company. However, there are a few reasons why trying to maximize your credit score in this way is tricky:

1. Different credit card companies report balances to your credit reports at different times. Many banks report your balance when they generate the statement, but some banks may report at a different time. To figure out your bank’s timing, you’ll need to look at your report monthly for several months and see if the balance numbers reported match your statement balances, or if they are different. If different, you’ll need to puzzle out when your balance was the amount that was reported.

2. Only the most recent credit card balance is on your report. Each month, when your bank provides a new balance for your report, it replaces last month’s number. Credit utilization is only based on the latest number. That means that if you do happen to figure out the optimal time of month to pay your bill to get your balance reported where you want it, it will only have a temporary effect on your score. You would need to consistently pay your bill at the right time each month to keep whatever score boost that you are getting.

3. The optimal utilization number you are aiming for is not known. Credit score formulas are proprietary secrets. Lower numbers seem to be better than high numbers, but too low is also not ideal.

The best advice I give to people about improving your credit score is to stop worrying about it. If you are carrying balances on your credit cards and paying interest, pay those cards off ASAP, and make sure you pay your card statements in full each month. If you have outstanding loans, get those paid off ASAP. If you do that and you make sure you always pay your bills on time, your score will automatically improve over time, and you won’t even have to think about it.

Finally, I don’t know what your score is, but it may already be higher than you really need.

1. You SHOULD pay off your entire credit card balance close or at BUT NEVER LATER than the due date.
2. Only overpay if you were stupid or desperate enough to get cash with your credit card. In this case you need to overpay so that the payment covers the additional interest on the cash withdrawal that accrued between the statement date and the payment arrival date. If you don't you get stuck with interest of the entire bill. It's a rather sneaky bank trick and can result in substantial interest charges and fees.
3. Impact on payment date on credit score will be negligible. An early payoff may give you a slight boost since it's good for the banks and bad for you, which is exactly the behavior that banks want in their customers.

Keep in mind: Credit score is not for your benefit, it is for the bank's.