How to isolate the constructor of class under test

In the second stage of AAA(Arrange/Act/Assert), we create the real class's object and call the real method which is supposed to be tested. But I have a class which has heavy dependencies across multiple layers of my software stack, and it is almost impossible to instantiate that class without having several pieces of application running. I cannot directly use 'new' keyword and instantiate my class under test.

for e.g. , I cannot use this kind of statements in my unit test.
ClassA a = new ClassA();

One suggestion was to isolate the real class's constructor. I wanted to know, how can I isolate my real class's constructor? Is there any other way to deal with this problem?