Welcome to permies Kristie.
Pictures would be a great help, as would be a location.
What is a pest where you live, may not be a pest where I live.
(You can add your location at your 'Profile' page. It greatly helps people in fine-tuning a response, or eliminating possibilities.)
We certainly want to encourage 4 year olds - they are our future.
We do NOT want him growing up with the impression that ALL bugs are bad.
So, the quicker we can find the problem, the quicker we can get him on the path to victory.
The greater success he has now, the more likely he is to become an advocate of 'growing his own solutions' in the future.
Holes in leaves are often an indication of 'creepy/crawly' things.
If you can somehow elevate the pot, that might be
enough to discourage the culprit.
Also, unless it is a 'dwarf' variety of sunflower, the pot may not be deep enough for its
root system.
And, as Matu pointed out, sunflowers are not the best choice for transplants.
Excellent choices for first time gardeners are radishes and carrots.
With many varieties of radish, 30 days from casting the seed, to having something to eat is possible.
(And, neither one requires Mom to cook it before it can be eaten.)
Children have rather short attention spans, so the quicker they see results, the more enthusiasm they have. It will keep their attention focused while the slower things are maturing. Starting with a 120 days to maturity crop is likely to be forgotten long before the rewards are seen.
Good luck