What gods would you believe in if you were born in Alaska....circa 2,000BC?

Hint: Alaska wasn't invented yet.

Some would argue that Judaism already existed
but of course that's not relevant to your question.

The correct answer is: none of us know. We don't know the (probably) many religions of those (probably) many, many different tribes that (probably) lived there at that time.

All gods were invented by man.

Animism, shamanism, and a pantheon of gods. https://en.m.wikipedia.org/wiki/Inuit_religion

Depends on how God worked His grace in their heart.

I would believe as the Holy Spirit was leading me to believe.

I lived with a native woman from a tribe that is in both the Yukon, and Alaska.  She was traditional, a shaman even, with a racial memory going back at least 10,000 years, and her God was much the same as the Christian one.  In fact, she became Christian pretty easily, without giving up her old beliefs.

You are right that Judaism (1300 BC), Christianity (33 AD) and Islsm (630 AD) didn't exist then. But Hinduism did (3200 BC). Either way I would probably believe whatever tribal cult was in that area. 

Hinduism existed then, but no one in Alaska would have heard of it. Same with the Canaanite religion that became Judaism. It existed, but only in a small, limited area.

the mighty Orca.... and the Great Bear........

'Tabaldak', 'Bmola', 'Kanati'.

I'd like to think I wouldn't believe in magic....

The elk. Or, is it moose in America? 

Whatever 

The same one as now.  Just because, and your date is debatable, it wasn't Judaism proper yet, doesn't mean God wasn't there.  

there might not have been any people 2000 b.c in those areas
and if you think about it. the flood was about 4000 yrs ago. which means there might not have been 7 continents in existence, and its said there had not been any rain on the land before Noah's Ark was finished.
so the question really is what religions were on earth and practiced in the days of Noah ! and if you think about it again, did eskimoes even exist !? because there were only 8 people on the ark and all tribes were not divide until after the day of peleg even when the land was divided into the continents and there mustve been a huge earth quake and probably the first stage in causing the higher mountains. maybe even one huge volcano eruption.
that said, i would think there was an idolatry among the followers of Cain, and whoever his successors were! these would be the children of perdition and worshipers of satan. the other group of people would be those that believed in the religion of Abel and Seth and Enos. there was pre-flood knowledge of Jesus Christ as a prophecy and a promise of his coming sacrifice to atone for the world, even in the days of Enoch and Noah. Noah was ordained by one of the early Patriarch to a priesthood that was called the Holy Order of the Son of God. and which was changed to the Holy Melchizedek priesthood after the Man names Melchizedek.

Enki, the God of water.

probably nothin because there was nobody there yet .. if you did it would probably be one of the chaldean gods from around Ur and Sumeria because that likely where your clan migrated from .. as did Abram, which is the patriarch of most of the major current religions ..

Neither Judaism or Christianity were invented. and Judaism was around