How can I obtain a Certificate of Eligibility for a VA Loan if the only documents I have are the NGB22 and the DD214?

If it's not in your OMPF, then you can get a copy of your NGB 23s from the National Guard state headquarters.

While not an option for you apparently (just mentioning it in case others happen by your question and it can help them), the Air Reserve Personnel Center (ARPC) maintains the records of USAF reserve components (Air National Guard and Air Force Reserves) individuals who separated after 2004. You can get them by doing a records request through myFSS*.

Your next option would be Defense Personnel Records Information service (DPRIS) on MilConnect*. Submit a request for your entire Air Force personnel OMPF (click on the "Request Personnel File" tab, then the blue "Request my Personnel File", and finally select "Air Force" for the OMPF system and click "select all" for the four categories in the "Document Index". It will take a few days, but whatever is available online will show up in your milConnect account.

Finally, if don't have success online, you can contact the Illinois National Guard headquarters*. States are required by law to maintain those records for 99 years.
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* myFSS - Air Force online military records - https://myfss.us.af.mil/USAFCommunity/s/login/
* DPRIS on milConnect - https://milconnect.dmdc.osd.mil/milconnect/protected/portlet/dpris
* Illinois National Guard benefits center - https://www.il.ngb.army.mil/Servicemember-Resources/Benefits-Center-ID-Cards-DEERS/

Reach out to your loan officer. I was having trouble obtaining mine through the online portal but my loan officer (USMC veteran) got it for me. DD214 alone should be sufficient.

https://www.va.gov/housing-assistance/home-loans/how-to-request-coe/

NGB form 23 was unattainable. However, I was able to track down my leave and earnings statements which coun towards my 6 years of Air Guard service in Lieu of the NBG23 because it shows all monthly payments and dates for all 6 years of duty.

The VA LGY staff are pretty responsive, you can call them directly at [login to see] . The VA home loan toll-free number operates Monday – Friday, from 8:00 am – 6:00 pm EST.

This is what OI pulled off of google.

An NGB Form 23 is a document that verifies the total time a National Guard member served on active duty. It is required when a member served at least 90 days on active duty, but not continuously.
To request a copy of an NGB Form 23, you can submit a Standard Form (SF) 180 to the state headquarters and branch where you served or were discharged. In Section II of the SF 180, you should check the block labeled "Other" and specify the document you are requesting. You should also include the purpose of your request in Section II, 2.
Here are some other documents related to the National Guard:
NGB Form 22
Confirms a member's character of service at the time of their discharge. It is the National Guard equivalent of the DD Form 214.
NGB Form 23A
An annual statement for Army National Guard soldiers that is issued when they reach their AYE. It is important for determining retirement eligibility and retired pay.