That isn't an example of "an object from another class". In your example the someDate variable is a local variable in class One's constructor. As such, any object assigned to it is unreferenced as soon as the constructor terminates execution, and that object becomes available for garbage collection. Nothing anywhere has (or can have) access to it after that moment.
I agree with Paul.
Here are my ideas on your case:
How would Class Two in the same package access the Date object someDate?
In class "One": 1. create a private variable "someDate " of type Date;
2. create a getter for "someDate" (can be "package access" if you want only in the package to be accessed)
3. initialize "someDate" in constructor (in your case: public One(SingleFrameApplication app) )
In class "Two": 1. create an object for class "One" by calling the constructor
2. get the value from "someDate" using the getter
If you don`t want to always create a new instance for class "One" I suggest you design class "One" as a Singleton.
Another option will be to declare your variable "someDate" as public static and initialize it in the constructor and then get it like this: One.someDate. I really do not recommend this way.