The quickest and easiest solution:
Use a bigger screw.
A larger diameter screw of the same length will fill the hole.
I have done this to hold my own dishwasher in, and in numerous other scenarios. I know a lot of cabinet material is crappy particle board which is not very durable.
Also, in cases where you are not worried about the screw coming out the other side (door hinges for example), a longer screw will work as well (and better).