As someone who has primarily gone in the other direction, my anecdata supports the opposite conclusion: static typing tends to help me to prototype over more dynamic languages, even if it takes (slightly) longer to physically write things down. I think this is because of two things:
1. If I'm prototyping things, I find I spend a lot of time trying to figure out what sorts of shapes the data in my program will have - what sort of states are allowed, what sort of cases are present, what data will always exist vs what data will be optional, etc. If I'm doing that in my head, I may as well write it down at the same time, and voila, types. So I'm not usually doing much extra works by adding types.
2. If I change my code, which I often do when prototyping (some name turns out to be wrong, some switch needs extra cases, some function needs more data), then that is much easier in typed languages than untyped ones. Many times my IDE can do the refactoring for me, and if that isn't possible, I can start making the change somewhere (e.g. in a type declaration) and just follow the red lines until I've made the change everywhere. One of the big results of this is that statically typed prototypes are often immediately ready to be developed into a product, whereas in dynamic languages, the prototype already bears so many scars from refactoring and the natural back-and-forth that comes from prototyping, that it needs to be rewritten over more from scratch. (The corollary to that being that I have never once had a chance to rewrite a prototype before releasing it to production.)
I can imagine that some of this comes down to programming/architectural style. I tend to want to define my types up front, even in dynamic languages, because types and data are how I best understand the programs I work on. But if that's not how you work, the tradeoffs might not be the same. The other side is that the type systems I regularly use are almost exclusively modern ones, with decent support for things like product and sum types, so that I can use relatively simple types to model a lot of invariants.