If you don’t know the type at compile time, then you can’t unbox because you have nowhere to put it – all you can do is store it in an object, which is: boxed.
The same also applies to reference-types like string: you can’t cast it to the right type if you don’t know the type at compile time: you have nowhere to put it.
You can special-case a few types, for example:
if(obj is int) {
int i = (int)obj;
...
} ...
Another trick that is sometimes (not often) helpful is to switch into generics; then instead of talking in terms of object you are talking in terms of T. This has… limited use though. The easiest way to do that is via dynamic, for example:
dynamic obj = ...
Foo(obj);
...
Foo<T>(T val) { ... code with T ... }
you can also add special cases to that appreach:
Foo(string val) { ... code with string ...}
Foo(int val) { ... code with int ...}
However, frankly I suggest it may be better to look hard at what you are trying to do.