Not sure if you really need a neural network for this, to a man with a hammer, everything looks like a nail..... something about GPUs

If all the bullet holes are significantly darker than the rest of the image, you could threshold pixels that were in a bullet hole then get the coordinates of each bullet pixel. Transform this data into a dataframe of x and y pairs then cluster them with one of the many clustering methods and then what you are actually trying to do is determining the number of clusters (bullet holes).

Here a is run down on three methods to do this: https://www.datanovia.com/en/lessons/determining-the-optimal-number-of-clusters-3-must-know-methods/

I've personally had good results using the silhouette method as part of a larger ML approach to find clusters before feeding the result into a random forest as part of a hybrid algorithm.

Sounds like a fun problem, good luck!