People who can break it won't spend the time breaking your homegrown crypto, so you won't get proof it's broken. But it's still broken. If lots of money or lives of political dissidents are at stake, it will be broken.
To have really capable people work on breaking your crypto for free, you have to be an insider. You become an insider by breaking other people's crypto. You can publish a break in an insider's crypto even if you are unknown. After you publish a few such papers, you become an insider and can publish your own crypto other people will spend their time trying to break.
People can learn the state of the art and develop an alternative to the common (NIST) choices which are no worse, but also no better. Some of those are blessed as "national pride ciphers" (GOST, Camellia, SEED, etc.).
Ciphers aren't the place where security most often fails. The failures have to do with implementation. More commonly, they have to do with implementation of protocols and systems using the protocols.
We're specifically talking about the scenario where you have a "tiger team" (strcredzero's phrasing) trying to break it. I interpreted GP as asking just how hard a time the tiger team would have if they don't have source code.
To have really capable people work on breaking your crypto for free, you have to be an insider. You become an insider by breaking other people's crypto. You can publish a break in an insider's crypto even if you are unknown. After you publish a few such papers, you become an insider and can publish your own crypto other people will spend their time trying to break.
People can learn the state of the art and develop an alternative to the common (NIST) choices which are no worse, but also no better. Some of those are blessed as "national pride ciphers" (GOST, Camellia, SEED, etc.).