Turn on cold water, hot water comes out first in every faucet.

May be pipes are close together so heat transfers...

You should check to see if the hot water pipe is too close to the cold water pipe. If it is, install insulation on the hot water pipe.

Changes

If you’ve recently had a new hot water tank installed or some other type of plumbing done, then hot water coming out of the cold water faucet might have to do with this. Call the plumber who did the job.

Replace Rings Or Clean Deposits

The rings inside one/more faucet might need to be replaced. They can wear out and water can cross to the other side, causing hot water to come out the cold faucet. Moen faucets are notorious for this. Also, mineral deposits can build up on the inside of the faucet and cause this to happen. This can be a problem only with one faucet transferring the hot water to all faucets. It's called "Crossfeeding".

We have the same problem in our house.... we know that the hot water pipes rest close to the AC ducts in one particular spot so we get really cold just before the hot starts to flow.

This sounds like the down feed tube in the hot water heater. The Initial cold water is the water in the line between the faucet and the hot water - normal. The hot water from the hot water heater is normal. Hot water comes from the top of the hot water heater while cold water goes down the feed tube to the bottom of the hot water heater to push the hot water out of the top of the heater. If the down tube is broken, cold water enters the top of the hot water heater and soon rushes out before the tank full of hot water. I had the same problem and took a copper tube inserted from the cold water intake. Problem solved for a couple of years. I hope this helps. Dr Fred

Do you have a radiator system for heat? Sounds kind of like our problem with a radiator system in one apartment we had. In early spring before settings were changed we'd get a back flow of hot water into the meter. Had to run cold to clear all the hot to get to cold again. Or do you have the heater set to very high temp?

think they have a mixer problem with every faucet?