How likely is it that the Air Force would grant a moral waiver for a domestic violence charge from nearly three years ago?

If an individual was charged with domestic violence, but there was no finding of guilt (i.e., charges dismissed, found not guilty, etc.), they won't need a waiver.

However, if there was an "adverse adjudication" such as entering a pretrial program, being offered a deferred acceptance of guilt, etc. then they would need at least a waiver for serious misconduct which would have to be approved by the Commander of Air Force Recruiting Service.

If they were convicted of domestic violence and the Lautenberg Amendment is applicable, then don't pass go, pack up and go home. No waiver will be given.
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ref: AFMAN36-2032 27 SEPTEMBER 2019 - https://www.af.mil/Portals/1/documents/2023SAF/PolicyUpdates/Military_Recruiting_and_Accessions_Upddate.pdf

Your posting under the rank of A1C, so your already in the service. Are asking because you going NCO? If so, the board might ask you about it, but, ultimately your already "in". The board wants to see what have you accomplished since you enlisted, are you a leader? Can you continue to be an asset to the Air Force.
How are your APR ratings?
Does your supervisors support you?
As for the actual arrest, non pro means without prejudice, ultimately, not enough evidence for the prosecutor to spend time and resources on.