I thought it was a huge jump but know I realise that it's less about Ash being an inventor and more about Ash rediscovering the ancient sciences that was left behind from the old world. This is, despite how it looks, a post-apocalyptic universe. The world has ended and people, without a hint of knowledge of the past, is just going through the same motions as humanity. However, the blueprint still exists; it just needs to be found and deciphered.
It seems like a huge jump to us is because this is technology we're absolutely familiar with. But in reality, this isn't that different from when Master Chief landed on a Halo. Just a really medieval version of that.