Do you actually know Kotlin? It has many features for DSL support, including operator overloading (though not the ability to invent random new operators fortunately), infix notation, a form of exhaustive pattern matching, extension functions, annotation processing, inlineable anonymous extension functions which sounds bizarre but actually is key to defining many DSLs in the language, and so on. It's a different approach to Scala but to say there's no way to do DSLs isn't right.

As an example, check out funKtionale. It's a library that adds various functional features like function currying and partial application to Kotlin, entirely by using its DSL features.