The problem I thought might arise involved a thought experiment.

An astronaut is in deep space. She measures the minimal effects of gravity, then measures time.

Another astronaut is 1,000,000 ly away. The gravitational effects are identical. He measures time.

It’s a thought experiment, so they have instantaneous communication. When they compare their time measurements, they are identical.

Would they be justified in concluding that time is linear globally?

There never was nothing.