Hello there! As your question is related to looking for identification/information regarding military personnel, our Guide on Military Identification may be of use to you. It provides a number of different resources, including how to request service records from a number of national agencies around the world, as well as graphical aids to assist in deciphering rank, unit, and other forms of badges or insignia. While the users here may still be able to lend you more assistance, hopefully this will provide a good place to start!

Sadly, you're correct that Army personnel records from that era were destroyed -- in a 1973 fire, which you can read about here: https://www.archives.gov/personnel-records-center/fire-1973

While that does mean that your father's personal military record no longer exists, there are other records that can help shed light on his service.

Morning Reports and Unit Rosters will help you understand the activities of your dad's unit. They may or may not mention him by name, but they will help you understand the experience of the unit as a whole.

As far as accessing those records is concerned -- unfortunately you cannot request copies of those records electronically or by mail. You have to visit the National Archives in person (or hire a 3rd party researcher to do that for you). You can learn more about accessing those records here: https://www.archives.gov/st-louis/other-records

I ran into a similar situation requisitioning records for both of my grandfathers. I received my grandfathers USN records (not destroyed) for free. When trying to get my other grandfathers set of records, I used a DoD portal where I filled out an online application. Someone mailed me an application stating it would cost a certain fee to mail them. I can’t remember the price. Have you tried the portal? Also, if you knew his unit, you can search for it. Often, these units are still active or have been absorbed by other units and they sometimes have historians or points of contact for any questions.