THE AKITU FESTIVAL - the ancient Babylonian New Year celebration - and its relation to Jewish tradition is the subject of an article in the Jerusalem Post:

Ten days in Tishri
By STEPHEN GABRIEL ROSENBERG

Shortly after Nebuchadnezzar II destroyed the Temple of Jerusalem in 586 BCE. he built the Ishtar Gate in Babylon. To him Jerusalem was a side show, take it or leave it, but the Ishtar gate was fundamental to his well-being and that of his people. It was the gate whereby the king and Marduk, the god of Babylon, would enter the city each year to inaugurate the New Year on the first of Nisanu (the Hebrew Nisan). It could only be done when the king and the god were both in the city, but it was the founding ceremony that would ensure the continuation of the Empire in good order for another year.

[...]

IN ANCIENT Babylon, the New Year festivities lasted for 10 or 11 days and there was a rather curious ceremony for each day. We do not know exactly what happened on the first day and the last days, but the royal inscriptions have preserved the rituals in between. ...

ONCE ALL this was completed, the New Year could commence! The culmination of this ritual took place at the Ishtar Gate, the northern gate into the city. Ishtar was the goddess of the moon, and of love and war. Not the consort of Marduk, the chief god and founder of Babylon, she was the chief goddess of the whole country of Babylonia and not just its capital. It is curious that the two deities mainly celebrated in this New Year ritual, Marduk and Ishtar, gave their names to the hero and heroine of the Purim story, to Mordechai and Esther.

Really not so curious as the Jews in Exile in Babylon, from the year 597 BCE onwards, must have been greatly influenced by their environment. ...

And what remains of the Jews who were there?

Many returned to rebuild the Temple in Jerusalem 50 years after its destruction, but it was destroyed again less than 600 years later, and now only the outer Western Wall remains. But in Babylon the Jews had absorbed the 10-day New Year festival, which they must have witnessed repeatedly, and which to them would have been a sign to reject foreign gods and to hope for the return to Zion, through the Ishtar gate.

Cyrus, victor of Babylon, gave them the opportunity. They brought back with them remembrance of the 10-day festival and applied it to their own New Year, starting on the first of Tishrei, and linked it with the fast of Yom Kippur on the 10th, to make that period the Ten Days of Teshuva (Repentance), which are still with us today.

Interesting thesis. Two comments. First, I have never before heard of the Enuma Elish being interpreted to say that Tiamat was raped, and I'm skeptical. Second, it's possible that the Akitu Festival influenced the Jewish New Year, but if so it's odd that the Babylonian festival is in the spring, close to the time of Passover, and the Jewish New Year is in the autumn. My own view is that Rosh HaShanah and Yom Kippur (the Day of Atonement) descend from a royal autumnal re-enthronement festival that can be reconstructed to some degree from the Psalms and which was salvaged and adapted in post-exilic Priestly circles after the Judean royal cult had been destroyed by the Babylonians. I would by no means rule out influence from the Akitu Festival, but it looks to me as though the basic concepts of the Jewish festivals could have been adapted from indigenous pre-exilic New Year traditions associated with the Judean Temple and royalty. These may well have ultimately been inspired by Babylonian models, but they would have been a fundamental feature of pre-exilic Judean society, not an afterthought brought in after the exile.