Are you asking about the historical or archaeological record? The earliest literature about deities, specifically the four primordial creators, comes from Sumerian texts that date to 28-2600 BC, though we only have them through reconstructions of later Babylonian and Assyrian sources. Objects from pre-literary societies, such as the Venus of Willendorf (which may or may not be divine figure in the way you're talking about) are much, much older: ~25,000 BC. Ceremonial burials, which also seem to suggest some preoccupation with gods and an afterlife, date back as far as 50,000 BC.

We obviously worshipped gods before this, but the Sumerian pantheon is pretty ancient. Sumer is basically southern Mesopotamia and we have archaeological evidence from the Early Uruk Period that suggests worship of the god Anu and the goddess Inanna at the Eanna District and the Anu District at Uruk. Enlil was the god of the air but he later becomes the patron deity of Nippur.

Some gods and goddesses are much older. There's the concept of the 'Mother Goddess' going back to Paleolithic worship, and there's the Indo-European sky god. But the Sumerian pantheon is one of the first defined group of gods and goddesses, due to the emergence of cities and writing at Uruk and Akkad.

EDIT: Early Uruk Period (c. 4000-3800 BCE), Oldest layer at Eridu has a mudbrick chapel (c. 4900 BCE)

There's different answers to this depending what view I take of what it means to know or know of a God. Many religions would argue that "knowing" a God does not equate to knowing a name of a God, any more than knowing the name "John" means you actually know anything about any particular guy names John. If we're just going with what's the earliest known name of a God, then that's something different again.

About three months back there was a post about the oldest name, and I gave some linguistic evidence suggesting that some of the oldest names we knew were the names of reconstructed proto-indo-european deities. Here's what I wrote here:

Now if you are looking for the earliest names we can recover, the place to look is in reconstructed proto-languages, for example try this list of Proto-Indo-European Deities. In it we have names like *Dyēus Ph2tēr which has come down as Zeus, Dios. this was a name back some time between 3700BC and, some have argued, maybe as far as 7 or 8 thousand BC.

Beyond this it gets tough. For example - what is the definition of a God? Is it creator? people argue no. Is it supernatural? how much power to a character have to be to be considered a God? To some degree this question is tied into a specific definition of what a "God" should be that artificially limits our answer, and even limits our conjectures (for example, combining ancestor worship with linguistic arguments, you could conjecture that a "god" named "father" was around as long as people have thought "what would dad do?"