Does anybody think it would be possible to make drinkable alcohol purely through chemical synthesis (no fermentation).

Certainly.  Fairly simple organic chemistry.  I've got an organic chemistry textbook on my bookshelf that covers how ("VOGEL") but I'm away from home at the moment so I cannot quote the method.  The real question is why?  Fermentation is simple, inexpensive and allows one to tailor the alcoholic beverage taste to suit the drinker's preferences.

Drinkable alcohol is ethanol C2H5OH.  Doesnt matter how it was produced.

6 hours ago, greenmansynthesis said:

Does anybody think it would be possible to make drinkable alcohol purely through chemical synthesis (no fermentation).

Yes you can make it.

That is not the problem.

The problem is that many (if not all) chemical synthesis methods produce by-products as well.

So your synthesis need to to include separating the desired products from the undesirable.

Particularly if methanol is a by-product, since methanol is poisonous.

So don't try it.

6 hours ago, greenmansynthesis said:

Does anybody think it would be possible to make drinkable alcohol purely through chemical synthesis (no fermentation).

But important to keep in mind that alcohols are a whole family of organic substances, in which there is a hydrocarbon backbone and one or more hydroxyl groups (-OH) attached. There is only one of these that can be drunk safely (within modest limits), namely ethanol, C2H5OH, as @chenbeier says. All the others are poisonous.

Commercial sprits are usually 40%  ethanol, the rest being water. Wine is about 13% and beer 4-5%. 

It is certainly possible.
https://www.chemeng.uliege.be/upload/docs/application/pdf/2020-06/article_publication_ethanol.pdf
but the search fore renewables means that the opposite reaction is actively being researched.

https://onlinelibrary.wiley.com/doi/10.1002/cben.201600025