You can definitely over test, but how can you possibly know what you built works (or still works when you change it for the 50th time) if you have no tests? There's a trade-off with testing. Early in the dev cycle, not testing can make you go super fast (supposedly, this hasn't been my personal experience but in general it seems to be true for teams). But you'll plateau quickly and then at iteration 1+n you'll just come to a screeching halt because you introduce bugs or the new engineer isn't confident that they didn't break downstream things and needs to manually test everything. Testing early will cause you to go slower earlier (again, not my personal experience but seems to be generally true of teams) but you'll be significantly faster at iteration 1+n.
I usually summarize this as: testing early will on average make your development faster over the life of your codebase. Knowing this you can make trade-offs. Not testing early is probably better called prototyping. It's OK to prototype in production if you need to. But know what you're getting yourself into.