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That difficulty is not accidental. It is the whole problem.
One approach would be to define thinking, then check whether a machine does it. But every simple definition creates another problem.
Thinking means processing information.
Then a thermostat thinks. It senses the temperature, compares it with a target, and responds.
Thinking means having a conscious experience.
Then there is nothing you can directly test. You cannot look inside another person and measure what thinking feels like to them.
One definition lets in too much. The other asks for something we cannot observe.
Turing chose not to begin with a definition. He replaced the original question with one that could be tested.