The character was first a toy from Ideal. Originally, CA could become "any" superhero (meaning of course "any" for which Ideal had a license). You'd buy the basic character in that blue and black costume, and then separately buy the kits for the other characters -- Batman, Superman, Aquaman, Captain America, Sgt. Fury, Spiderman, the Phantom, the Lone Ranger, Buck Rogers, Flash Gordon, a few others.
The comic book retained the name and the costume, and in a few panels of the first or second issue, the "Silver Streak" amphibicar, but NOTHING else from the toy line.
The concept in the comics was that CA was archaeologist "Clive Arno" (apparently somehow with Bruce Wayne level money and scientific skills) who with his associate "Krellik" (a Luthor lookalike) discovered a strange site: In a single location, it showed evidence of a dozen or more different cultures from around the ancient world. They came upon a cache of coins, each bearing the face of a different ancient god.
When Arno buffed the coin of Vidar to a pristine shine, he suddenly felt strange, stumbled out of his tent, and somehow realized he could almost effortlessly lift their Jeep over his head.
To speed up the process of cleaning the coins, he and Krellik used some kind of "ionizer" machine. Apparently the beings that left the coins anticipated just such an action, because the energy triggered an immersive holographic message. The "gods" were actually extraterrestrials called "Apsu." They had decided to leave the earth, but elected to leave behind tokens of their presence and power, mainly the coins, which would imbue any *worthy* holder with many of the powers of the featured deity. (Of course, being DC, especially in the '60s, they couldn't have a hero more powerful than the Big Blue Boy Scout, so CA could only have the powers of six gods at a time, because he could only carry five coins in the compartment in his belt, plus one in the lining of his hat -- even though one would have thought the wisdom of Odin could have come up with something WAY better than that. And in the third issue, they "depowered" him even further by having all the coins except four get lost in an earthquake. He kept the three that fused together -- Zeus/Thor, Herakles/Vidar, and Heimdall -- and gave his son Hermes/Hermod, basically turning him into another Kid Flash.)
One thing that seriously annoyed me even as a kid was that the writer decided all the gods from all the pantheons were really the same, but known by different names. So Zeus was Thor, Vidar was Herakles, Ares was Tyr, etc.
The series only ran for five issues, and apart from the first issue, maybe the second, I don't recall any other evidence of the larger DC continuity.
The "New Gods" quadrilogy (Is that a word?) originally ran only about a year (less for a few titles, 14 months for Mr. Miracle, IIRC). But the characters and approach influenced DC forever.