You could look at Wise, you will get a US Bank Routing Number and Account number individual to you which you add as Wire Transfer destination in E*Trade for $ transfers. Unfortunately, it's still Wire Transfer (so you get hit by that E*Trade fee) but it's in US$ and then once it's in Wise you can exchange it there for better rates than E*Trade or your EU Bank account.
Or you can transfer US$ to Revolut and convert it there into € at your own leisure which again might be a better rate than E*Trade.
Unfortunately, all of that will attract the E*Trade Wire Transfer fee (unless you are lucky enough that that fee is 0$ because you have an Employee Stock Plan account that is exempt).
To use the ACH option in E*Trade you need a full US bank account that you can link electronically, otherwise Wire Transfer Fee hits at least from what I understand.