Automated unit test generation consists of two complementary challenges: Finding sequences of API calls that exercise the code of a class under test, and finding assertion statements that validate the behavior of the class during execution. The former challenge is often addressed using meta-heuristic search algorithms optimising tests for code coverage, which are then annotated with regression assertions to address the latter challenge, i.e., assertions that capture the states observed during test generation. While the resulting tests tend to achieve high coverage, their fault finding potential is often inhibited by poor or difficult observability of the codebase. That is, relevant attributes and properties may either not be exposed adequately at all, or only in ways that the test generator is unable to handle. In this paper, we investigate the influence of observability in the context of the EvoSuite search-based Java test generator, which we extend in two complementary ways to study and improve observability: First, we apply a transformation to code under test to expose encapsulated attributes to the test generator; second, we address EvoSuite's limited capability of asserting the state of complex objects. Our evaluation demonstrates that together these observability improvements lead to significantly increased mutation scores, underscoring the importance of considering the class observability in the test generation process.