Are there any other formula of average acceleration beside change in velocity over change in time?

Simply put, no.

You can change the units used, but the fundamental relationship doesn't get any simpler (or more complex). Velocity is Distance unit per time unit. That's ALL we have to with. is a rate of change of that fundamental combination, still in terms of one of them - time. Velocity = m/s Acceleration = ##m/s^2##