depends what you mean by genes. I assume you've already googled it.
DNA undeniably exists, you can even separate it out yourself if you have the time and energy. it's a common middle school lab experiment.
there's very good reasons to believe sections of DNA correspond to traits expressed in organisms. We call those regions 'genes' as they seem to make up discrete units within genetic material. There's even 'start' and 'end' sequences which seem to denote the specific units. In reality it gets a lot more complicated than that and it can sometimes get fuzzy what a 'gene' actually is, because a specific trait's expression might be governed by a multitude of factors including WHERE that gene is on the genome, so it's not as simple as saying 'this genetic code gives you this trait' in all instances
but all that aside whether or not genes 'exist' in the sense of some absolute isn't a terribly important question. the idea of genes is useful, and helps us make predictions, and the idea seems to hold up pretty well to experimentation, so it's easier to just assume they exist. getting tied up in the semantics of what does or doesn't exist usually isn't very productive. does the concept of the number 2 exist?
