Pay order only after it been placed and validated
The standard approach here is to use the payment information to create an authorization for as much as you will need assuming the order is to be placed. If it's for $100 of custom merchandise, you authorize a $100 charge on the customer's credit card and then capture it after manual review. This is very typical and in many places a requirement - the idea being you can only authorize payment during checkout and capture it once the order has been shipped.

How the authorization + prior authorization capture flow works will depend on your payment gateway and the methods of payment you're accepting, but most should support this. (I don't have direct experience with Russian payment gateways if you're developing this for a Russian merchant, though.)

In your case, you might just include a message on the checkout form that the customer will see the payment authorization but will not have funds debited from their account until the order has been manually approved by an administrator. There is no automation that I'm aware of in Commerce 2.x core for capturing prior authorizations on specific state transitions, but that's something you should be able to include in your site's customizations module. Again, the exact process there will be very dependent on your payment gateway's API.