No, it is not possible to determine the thermal equilibrium between two objects in contact without knowing their temperatures beforehand. The concept of thermal equilibrium is based on the idea that two objects are in a state of balance, with no net heat transfer occurring between them.
In order to determine if two objects have achieved thermal equilibrium, you would need to measure their temperatures and observe if they remain constant over time. If the temperatures of the objects stabilize and do not change, it indicates that they have reached thermal equilibrium. However, without prior knowledge of their temperatures, you cannot conclude whether thermal equilibrium has been achieved or not.
Temperature measurement is an essential factor in assessing thermal equilibrium. Without temperature information, it is not possible to make a reliable judgment about the thermal state of the objects in question.