Is it possible to buy the AirPod Pro's without the case?

Replacement instructions for Airpods are provided at the bottom of this support article "How to find your lost AirPods, AirPods Pro, or AirPods Max": --> https://support.apple.com/HT207581 Neither the warranty nor AppleCare+ helps with the cost of Airpods that are lost or stolen. The cost for damaged Airpods may be lessened by any 'AppleCare+ For Headphones' coverage you may have.

'AirPods Service and Repair' lists replacement fees. Click here --> https://support.apple.com/airpods/repair/service

1. If you can't find your AirPod or Charging Case, or if something is damaged, get the serial number. Click on this link to discover how to find the serial number. --> https://support.apple.com/HT209371

2. Contact Apple Support for a replacement. Click here --> https://getsupport.apple.com/?caller=kbase&PGF=PGF32003&category_id=SC0298

(You may have to go to the support article in my first link for the special Airpod replacement service link if that one doesn't work.)

3. Learn how to set up your replacement.

Set up your replacement AirPods or charging case - "When you get your replacement, follow these steps to use your AirPods again." --> https://support.apple.com/HT207827

I don't think the question was answered. Could someone just purchase the airpod without purchasing the case also?

There is a fine distinction between wanting to buy Airpods if you already owned them but lost them and wanting to buy them without having owned any already. Apple provides a replacement service. In your case you would want to buy them and I don't think Apple sells them alone.

They don't.