Have you had someone else start the car and you being under the hood yet? If not please do. If you have please discribe where that noise is exactly coming from, exactly what it sounds like and how long it last.
I had a sound on one of my cars like that. In my signature you will see the Ponticrap, well my G/F the animal killer decided that a transmission killing rock in the middle of the road was a rabbit and torched the trans pan, the oil pan and almost put a hole in the floor pan.
Well, she drove home 1 mile leaving a trail of fluids all over the road. When we replaced the trans pan and the oil pan, she said that she had a sound when she started it cold.
Turned out it was the lifters and the rods were toasted and the engine got replaced by the insurance company.