It's very possible. The Jews could likely have done this. You actually took the easy way out.
By finding something that looked like what the Jews developed, you "found" a "menorah." This is something that is quite logical. We don't know, of course, but it is possible. However, that I do want to add the following about why this is funny altogether...especially since Chanukah (Hanukkah? Kanike?--Yes, that last one is a real spelling. Yikes!)
A Confusing Text in Hebrew that Doesn't Read "Straight" and "Is Missing Pieces"
What I hate about English translations of the Bible is that they sound like Cecil B. DeMille is trying to make a religious movie out of it--stuffy, proper, showy, well-designed, on-stage. It doesn't take a scholar or academic to learn Hebrew or Greek. You can learn to pronounce the letters of either in about an hour or two and be reading in an afternoon. Hebrew especially is very simple. The rules never change.
But expect be disappointed sometimes. The Bible doesn't read the same in the original languages as it does in the translations. Ever heard of "lost in translation." This is sort of the opposite. While you gain a lot of insight, you also lose the fakery and puffery those versions of Scripture often try to "frost" the Bible with.
One of the parts of the Bible that they do this to is the part of the "menorah," Exodus 25:31-40. You think you know what a menorah is, right? It's because you've seen one.
Or, you think you have. That is why you think it looks like what you pictured above. (You just think you found what looks like a "menorah," but you just wait!)
Ha ha ha. You're wrong. Guess what. This is one of those parts of the Bible that when you learn to read the original Hebrew it will leave you scratching your head: "Did I not learn something correctly? Is my Hebrew Bible missing something? Maybe I should ask somebody something about this." Bits and pieces seem to be missing. It seems to be saying things again and again and yet nothing. You read words and words and words and yet you read nothing. You end up just wanting to rip the words up and eat them so you can poop them out.
Yep. If you don't understand what you just read and can't describe what was described to you when you get to it, then you read it correctly:
The menorah is described in great and even confusing detail two times in the Torah. This is an almost compulsive word picture, whether in translation or in the original Hebrew. The constant repetition of the need to have almond-shaped cups, bulbs, and flowers is especially opaque.--Menorah, It's "Branches" and Their Cosmic Significance: TheTorah.com.
It's the oy-vey of Bible reading. According to a metaphor in the Midrash Tanḥuma, the reason why it reads so confusing is that when God showed him the object and wanted him to write down what he saw, Moses himself didn't know what he was looking at. Nahmanides also agreed, as did the twelfth century scholar Moses Maimonides (whose name may sound similar) and drew schematics that looked similar to giant those Chanukah menorahs you see today placed around cities and towns that have angular shapes instead of curved arms. (It looked like something out of the 1960s space age instead of the Middle Ages--not kidding!)
One of the reasons we accept a seven-branched "curved" arm menorah is not because the Jews originally created such one for their Temple or borrowed such from heathens or pagans (though that would have been a good idea--and they might have if they were smart). But it appears the idea came from something as simple as a lack of space.
What Do King Arthur and King Solomon Have in Common?
While King Arthur is a legendary figure, there is a tiny bit of historical evidence that suggests that he may be based on a genuine Saxon hero of the past. The same is true of King Solomon. It appears that while we have some evidence that he was a genuine son of David, everything else we know about him is legendary--yes, even in the Bible...and that means all the stories about his kingdom and the Temple.
This means there was no menorah--at least no menorah from Solomon's Temple like you imagine (sorry, JWs).
We do know that there was one from the days of the Hasmoneans--you know, the one's who gave us Chanukah (though the "miracle" of the 8 days is another story). By their time we believe we might have a menorah similar to what we know today. Did they just get one from the heathens by then? Not likely since they just had that war with Antiochus IV Epiphanes and purged everything out of Judea that was not "Jewish." So where did it come from if Solomon was a legend?
The earliest image of a menorah appears on a coin of the Hasmonean Mattathias Antigonus (39 BCE), who minted a small bronze coin. It is after that that the "common" image of the "curved" menorah becomes the standard.
Was this the menorah that was always the type the Jews used before? Who knows. But it fits on a coin--and thus it became the "emblem" of a nation. Not the Star of David, but the menorah.
And that is likely how it happened. The coin, which was how the ancients of the time advertised their king or ruler, shaping their idol image, was used to shape the menorah. Other nations could put an image of the deity/ruler on their coins. But Jews would not. Their stamp was the stamp of light, the light of liberty.
When the Romans took the sacred things from Herod's Temple, they purposefully marked the Arch of Titus with this image of liberty and light, the Menorah, to show that the Jews had been conquered. If you note, the menorah was shaped like that found on the coin of the Hasmoneans:

