I will try not to go with a whole rapid progress but a nation 60 years established would possibly have a large navy by now.
Unless its set in the post-apocalypse. The NCR in New Vegas has existed for more than 60 years, is well established, and as far as we know has no navy whatsoever. They barely have an air-force.
Now given that this is a convention, saying "No navy" would be limiting what we can do substantially. But that doesn't mean we can't tone it down a bit and keep it somewhat grounded. I'd say recommissioning old pre-war naval vessels is fine. Which is what the rest of us are doing, but building your own brand spanking new ones? No. Not at this stage anyway.
Like I said, Aurodium selling old U.S. navy ships is at least sort of plausible (sort of). But having your nation already be pumping out full first world navies and selling them off like its nothing is just silly.