Distilled alcohol was first documented by 9th century Middle Eastern Muslim chemists, centuries before its appearance in Europe. The earliest reference I could find appears in the medical literature of the Rambam.
In the third chapter of his Treatise on Poisons and Their Antidotes, originally written in Arabic (Maqālah fī al-sumūm wa-al-mutaḥarriz) on the request of a Cairene vizier in 1198, the Rambam refers to the newly invented (and now very popular) liquor we call Arak. He previously recommended taking certain medicines with wine, but since his Muslim readership could not drink wine, he also advocates using this aniseed-distilled drink (in the original Arabic: أنيسون). Here's how Moshe Ibn Tibbon translated it into Hebrew in the 13th century (Samei Hamavet Ve-Harefuot Kenegdam), with an English translation below by Gerrit Bos, a scholar of medieval Jewish medicine:
והרפואות אשר זכרו הרפואים, מהם מה שצוו לשתות ביין והם במים ומהם בחומץ ומהם בחלב. ואני רומז על מי שנשכו מי שלא ידע מינו, שיעיין ענינו... ואם מצא קור חזק, כמו מי שימצא אצל מי שנשכו עקרב, שיבחר מן הרפואות הן, מה שליקח ביין.
ומי שלא יותר לקיחת היין, יקחם בתבשיל האניסון, כי האניס, הסכימו כל הרופאים, שהוא מועיל מכל ארסי בעלי חיים
Some of the remedies mentioned by the physicians should, as they order, be imbibed in wine, some in water, some in vinegar, and some in milk. As for myself, I advise anyone who was bitten or stung by an unknown sort of animal to examine his condition....If he feels a severe cold, as someone feels who was bitten by a scorpion, he should choose from those remedies which are taken in wine. If someone is not allowed to take wine, he should take what he selects from them in an anise decoction, because all the physicians agree that anise is beneficial against all animal poisons.
Throughout the treatise, the Rambam repeatedly use the phrase that "those who cannot drink wine should use an anise decoction," strongly implying an alternative alcoholic drink.
Since we're already on the subject, in his Treatise on Asthma (Maqāla fī al-rabw), the Rambam equates wine with nabīdh, a general term for intoxicating beverages, which "fill the head and are harmful to the brain and heat it...to the point of drunkenness." Despite these warnings, the Rambam gives a recipe for a nabīdh in his Treatise on Marital Relations (Fī l-jimāʿ), again translated here by Gerrit Bos:
يؤخذ سلجم وجوز وتين و يطبخ طبخا جي ّدا و يص ّفى
ويلقى في ذلك الماء زبيب من ّقى من عجمه ويطبخ طبخا جيّدا ويص ّفى ويلقى في ذلك فانيذ ويترك حت ّى يغلي و يصير نبيذ و يشرب
Take turnips, walnuts, and figs; cook them well in water, strain this and throw pitted raisins into the water. Cook this well, strain it and throw fānīdh [a kind of chewy sugar-candy] into it, and leave it on the fire until it boils and turns into nabīdh; drink this.
And yet another:
واعلمأ ّنالأطبّاءإنّمايطلقونشرابالمفرحعلىشرابلسانالثوروحدهوقدجرّبواالمتق ّدمونهذا وهو إن يلقى شيء من لسان الثور في النبيذ و يتركه حت ّي تخرج قوته فيه فيجدوه يز يد في الفرح ج ّدا ويقوّي على الجماع. وإذا أخذ ماء الحديد المعلوم وغلي فيه لسان ثور أربعة دراهم قشر أتر ّج نصف
أوقية قرنفل مرضوض نصف درهم ومزج بهذا الماء رطلين خمر أو رطل عسل نحل لمن لم يستطيع الخمر وشرب ذلك أ ّولا أ ّولا نفع نفعا كثيرا.
Know that the physicians only apply the name “exhilarating drink” to the drink prepared from borage. The ancient physicians have tried this; that is, if one puts some borage in nabīdh and leaves it there until its strength is extracted, one finds that it greatly increases pleasure and strengthens the lust for sexual intercourse. And if one takes the well-known iron water and boils in it four dirhams of borage, half an ounce of utrujj (citron or lemon) peel, and half a dirham of crushed clove, and mixes with this water two raṭls of wine or one raṭl of bees’ honey for someone who cannot take wine, and drinks this little by little, it will be greatly beneficial.
Do these count as examples of distilled alcohol? This might not be the Judaic source you had in mind, but I think it precedes halakhic literature that discusses other kinds of distilled alcohol.