How to get all orders by custom column in sales_order table using API

I’m using a module allows user to select delivery date and time slot while placing the order. Module that I use creates additional columns in table sales_orders

For some business needs I would like to use an API to develop an integration with external system. To do so I need to fetch all orders by delivery_date

I have been trying to find some solutions, one of them was to use external_attributes, however searchCriteria for /order endpoint doesn’t support it. I been trying to get all orders that has been placed and then just filter the response array. This is not efficient as database grows and eventually I’ll end up at the point that request will be too big to go through.

I don’t really know how I can approach this problem.