Whining noise when car is cold. Engine rebuilt and most pumps recently replaced.

[Dave333]

Hi, wondering if anyone can help me. My car makes a whining noise when it starts up (videos attached). I’ve replaced most pumps and due to a faulty timing belt kit, my mechanic has also recently rebuilt the engine. The sound seems to be coming from the back of the engine bay. I was hoping the fact that it doesn’t start until a few seconds after the engine starts might be a clue?

Any help much appreciated!