I think this is a really interesting, if somewhat philosophical and unanswerable question.
There are certainly valid arguments for the idea that math could not exist without science OR that science could not exist without math.
The fact is that what we need is a historical answer, that we just don't have. Did early humans begin counting and adding because of some scientific need? (food, hunting, movement of their tribes?) or did the ability to use math lead to the use of science? We can never know the true answer and as in most situations, the likely truth is somewhere in between. Science and math are clearly intertwined in a way that we cannot separate, becoming more and more so over time. Likely early humans needed basic math and science skills that they used together to survive.