Could genes exist if the theory of evolutionism would be untrue?

Evolutionary biology is not a monolithic theory. Few creationists argue against genetics. The only question is whether genetics alone is enough to account for the biological diversity we see today. Could a tiger and a salmon have a common genetic ancestor? Could the complex mechanism of DNA, the foundation of life, have come about by accident? Those are not currently answerable by science with certainty or rigor. But genetics (along with epigenetics) is enough to answer how a child will be like his parents, or how wolves could have become domestic dogs, or even how marine lifeforms could have adapted to land and flight.