Sorry but this is not so. All you need is genetic variability in a population to produce new traits, none of which came from mutation.
What if none of the existing genetic variability could produce the new trait?
For example, you can start with a bacterial population of just a single bacteria that has no resistance to antibiotics. Over time, mutants appear over time that are resistant to bacteria. How do you think that happens?
Remeber that bacteria are haploid organisms.
The fact that any small number of individuals out of a large population will form a new population in which new gene frequencies develop their own group traits as they breed among themselves in isolation from other populations.
How do you explain features that develop over time that are not found in the initial gene pool of the population?