For US citizens, Turkish eVisa's are nothing more than a formality. No details are asked during the application process beyond the basics like your name and passport details, and their approval is automatic once you have over your credit card details.
There is absolutely nothing stopping you from applying now, as long as your planned entry visit is within the 6 months validity of the visa. The Turkish eVisa site confirms this :
Do I need to enter Turkey on the exact date specified in my application?
No. The validity period of your e-Visa begins from the
date specified in your application. You can enter Turkey on any date
within this period.
However as a general recommendation it's probably better to wait until closer to your trip. The main advantage of this is that it will give you a later end date for your visa, which might avoid you needing to get another visa if you decided to return to Turkey within 6 months of when you apply. The second advantage is that if for some reason your trip doesn't go ahead, you will not have wasted the money for the visa (although at only $20 that's not a major issue)
There is one potential benefit for applying early. There is a history of visa issues between the US and Turkey, and for some time in 2017/2018 Turkey suspended issuance of eVisas to US citizens. Whilst there is no expectation that this will occur again, applying now will guarantee that you would not be affected if something like that did happen.
Personally I normally apply for Turkish visas a day or two before I arrive, although I have applied as late as a few minutes before passing through immigration (literally whilst standing in the immigration line!) without any issues.