We want to be able to take payment without creating an order. The record should be maintained in orders > transactions or any other panel. Very much like a donation.
To make a payment, you need to make a transaction. It can be for any type of product, viz virtual, downloadable etc.
So, in my opinion, if you want to take payment like donation etc., you can create a virtual product (with Visibility: Not visible individually).
Then create a custom form in the frontend for taking payment. On the form submit, send a request to a custom controller, where you can place the order programmatically.
Also, you would need to rewrite the email template for your custom order to make it different from the default Magento's orders.
Additionally, you can create a custom table to keep a record of such payments, so that you can generate custom reports.
Please let me know if you have any other question.