There really isn’t any way to force them to make a payment, but what you can do is mark the record as “paid” if they do make the payment.
This is not a simple thing to do technically, because after they make the payment, you need to know the ID of the Participants Database record they just created. I don’t know the specific steps to take to do this, I’ve never done it before.
The general idea is that when they go to make the payment, you are somehow saving the ID of the Participants Database record. Then after the payment is made, there is an action that is triggered. You put a function on that action that updates the Participants Database record. I don’t know the details, but it is somewhat complex.
I do offer an add-on to Participants Database that is for the purpose of taking dues payments for members. It uses PayPal, so if that is OK, you may want to check it out: Participants Database Member Payments
Alternatively, you can use a different plugin altogether to manage your members and payments, there are several that work as add-ons to WooCommerce if you want to stick with that.
Thanks a lot for your detailed answer. I also think that forcing the payment in order to validate the record seems to be complex and needs coding.
Your suggestion of using the Participants Database Member Payments is not relevant, as we need to use credit cards and PayPal as optional payment means.
Maybe I have to dig into different plugins managing members and payments. Thanks again.