Did the ancient Israelites teach that other gods didn't exist or were just not to be worshipped?

Both. There were lots of different Israelites living over the course of centuries. Some parts of the Hebrew scriptures point to one view, some to another.

The first commandment, "Thou shalt have no other gods before me," as others have suggested, implies that other gods are out there, but not to be worshiped among the Israelites. When Moses confronts the Egyptians, their priests are able to work miracles too (their staves turn to snakes, etc.), only Moses' miracles are more powerful, again implying that what's happening is a power contest between gods. Psalm 82 depicts Yahweh sitting supreme in an assembly of gods (chewing all the others out for their injustice).

Other passages, though, depict the other gods as fictional. When Elijah confronts the priests of Baal on mount Carmel, Baal conspicuously fails to deliver any display of supernatural power at all, and the prophet mocks his opponents, suggesting that maybe their god is asleep or off on vacation. Passages like Psalm 115 or Isaiah 40 explicitly state that the idols and gods worshiped by others are merely objects made by their own hands.

The word translated "jealous" can also be translated "zealous," by the way (even in English, you can hear how closely related they are). It means that God demands exclusive attention. That doesn't necessarily imply the existence of other gods, but merely of other things (like idols, or mere worldly distractions) that might draw the worshiper's attention.

They worshiped ONE god and believed that others existed. The god that they worshiped was THEIR god.. the God of Abraham.

Today's Jews for the most part believe that the god they worship (or acknowledge) is the same god as the one that the Moslems worship (Allah, an ancient Moon god of the desert people). It is "politically incorrect" to say differently, so they don't bother. If you ask a RELIGIOUS and EDUCATED-IN-THE-BOOK Jew, you will find that the VAST majority don't believe that they are the same.

This is very similar to the Mormons. To days Mormons have NO idea that the original belief was that there is more than one god and it is just that they worship ONE god out of that number. Most wont even publicly admit that they believe that humans can become gods themselves.

The old testament never said that other Gods don’t exists, just that they are not to be worshiped (by the Jews) so I have to think that since Christian ripped off the Torah that the Israelites didn’t think that other Gods where fake. But the Israelites weren’t the monotheist the Ancient Egyptians where, at least for a while.

Good question-I'm going to say "Thou shalt have no gods before me" clearly acknowledges that there are other gods-just that they are not to be ones #1 deity. I don't see any other way to read it. I guess that explains why they could go in for paganism so quickly when Moses went up the mountain. Moses was very upset with them when he got back, but obviously-they must have had that inclination in the first place.

I think the whole logic of strict monotheism came later, hence Christians ended up with Trinitarianism as a bit of a fudge.

You've gotten a lot of answers, but none of them cites any scholarly sources.

If you really want to know, there are many, many professionally-written books about the history of Judaism. The ancient Hebrews' ideas about God (and about many other things) changed over the centuries. So, for one thing, you need to specify which period of history you're asking about.

Go read a book on this very complex subject by a real historian instead of listinging to guesses by amateurs here.

The taught that they were not to be worshiped commandment #2 You shall have no other gods before me

there were the fallen angels callings themselves gods, also the word in the original language given in the old testament for god is Elohiem which is plural for gods.