You have to eliminate and then isolate. Have you turned off the pump and closed valves to eliminate the circulation system?
Shut off all valves to all water fixtures including the washer. DW can be left alone. Shower valves if possible.
One at a time open the cold valves at one fixture, run the cold water And see if it's hot. If not open the hot valve and run the water.
Do you have a touchless kitchen faucet? Bath and shower valves can cause a cross over. The tempering valve might be stuck allowing hot water to cross over to the cold.
What is unusual is the cold is hot at first. Cold water lines always have higher pressure than hot water lines. Cold water will mix with the hot and push out warm water at a water fixture.
