If a constructor can fail, don't make that constructor public. Instead, add a trivial constructor to allocate an empty instance of the object, then make your possibly-failing constructor a factory function that takes whatever arguments you would pass to the constructor and returns an error code. The object being "constructed" should then be passed by reference as one of the arguments to the factory function and filled in. (If you're writing this in Rust, you have better options, since you can explicitly take ownership of some of the factory function arguments and avoid the need to allocate a trivial instance of the object by returning it as one of the variants of the sum type Result<T, E>.)

Note: I don't actually know C++ very well. It's possible there's a more idiomatic way to accomplish this. In particular, another wrapper class could be created that owns an instance of the trivially-constructed instance mentioned above. The factory function could then take an instance of the wrapper class and then modify and return an instance of the class you actually want to obtain.