You have to have a flat population over long timescales. If you started with two tyrannosaurs and had a population growth rate of just 0.02% (population doubles every 6600 years), there would be approximately 500 billion tyrannosaurs on the planet at the same time by the point they went extinct.
It's likely the population fluctuated up and down slightly on short timescales, but the average would have been constant. They were spread out over a continent so any disruption would need to be very widespread to take them all out - which eventually of course is exactly what happened.
Humans are unique in that we can develop technology to exceed our carrying capacity.