Noah preaching on a telephone

This is a common misconception about the Cambrian Explosion.  Obviously, the Cambrian comes after the Pre-cambrian era and is the first period in the Paleozoic era.  The period covers 53 million years beginning about 543 till about 490 million years ago.[1]  

• 543 mya - First shelled animals
• 540 mya - First arthropods
• 535 mya - First chordates
• 530-520 mya - The Cambrian Explosion - The first brachiopods, gastropods, cephalopods from the phylum, mollusca; the first sponges, the first echinoderms
• 520 mya - Cambrian mass extinction 40-50% of marine genera go extinct 
• 490 mya - By the end of the Cambrian all phyla exist in the fossil record.[2]

If one means every phyla known to man, then yes, every phyla is present in some form in the Cambrian.  However, in the Cambrian you have the phylum, chordates, and within that phylum you have the vertebrate class, fish.  That's it.  The only vertebrates are fish.  Jawed fish don't show up in the next period, the Ordovician.  It is not until, the following period, the Silurian, that jawed fishes appear in the fossil record about 47 million years after the Cambrian ended.  Fish are still the only class of vertebrates in the fossil record at this point.  However, the first land fauna appear in the fossil record also during the Silurian: millipedes, spiders, and mites. [3][4]

The Cambrian contains the fossil record of the first chordate.  True, every person anyone has ever met has had a hollow dorsal nerve cord, a notochord, a pharyngeal slits, an endostyle, and a post-anal tail sometime during their life, but so has every fish, chicken, and cow every person has eaten.

There are no chordates in the fossil record other than fish until the Devonian, 70 million years and three periods later.

Even Brian Thomas proposes a simpler explanation.

Maybe some ancient coal melded around a piece of modern machinery from Khakasis. Maybe an old explorer dropped an even older bronze bell down a well for miners to later extract from the mountains of West Virginia. And it is perhaps conceivable that coal somehow enveloped a more recently manufactured iron cup. These and other apparent human artifacts embedded in coal need more investigation.[5]

If you want to smelt an aluminum gear like that one, you need electrical power. If they could make that aluminum gear, Noah could have preached on a telephone. [6]

They know this is wrong.

They know this is wrong. All phyla are not present in the fossil record till the upper Cambrian. Also, you are ignoring the vast time frame of the Pre-Cambrian fossils.[1] [2] It is the genetic studies that push the phyla before the fossil record.[3]

Also, what does it prove to have chordates when you believe that Cambrian chordates swam with whales?

I could also note that the Theory of Evolution does make predictions about the fossil record, but not "the fossil record would start with one type of animal life, increase to two, and so on." Fossilization is a rare event. The theory assumes that the fossil record will always be incomplete. This assumption has been part of the theory for a century in a half. ICR knows this.