You can't, there could be a closed source curve parameters, but it would be useless because G can reveal start and range of the group order.

I was thinking about a provable algorithm which could be placed on a computer to randomly generate a curve and then produce a closed source library, then we could burn that computer so that nobody can access any data from it.

But as I said, it won't work, and I'm not sure doing that is even possible.  I know this sounds stupid, hence the need to ask it from those who'd know better.