Customer's Starting Balances

My question is this:
For instance before starting using in my business i had my customers to whom i sold some goods on credit terms. They are supposed to pay the money now and i need to fill their payment information in my business. Now how can i record the received payments for the transactions that occured before using this accounting software, manager so that i can determine customers amount paid even for the past days. Or how to record the past credit money in to know how much total the customer need to pay

Yes, if an invoice has been partly paid, enter only the receivable/outstanding amount.
Read the following guides:

Set starting balances for customers | Manager

Set starting balances for suppliers | Manager

Set starting balances for inventory items | Manager

Enter starting balances | Manager

Fix starting balances | Manager

Read the entire guide: Guides | Manager

My main aim is to know how much each customer owes my business before the beginning of financial periods. But i want to do that without recording the sales invoices but rather just setting each amount the customer owes you so that once payment is made, it shouldnt affect the current months’ profit and loss

You can’t - if a customer owes you money, you have to record the unpaid invoices (you could use just one invoice with the total) with the invoice date set to before the accounting period. This way the invoice amount does not have any effect on the period’s sales and profit & loss account but is recorded in the opening balance on the balance sheet

This is clearly explained in the guides above