I seek an early source that giving Kiddush (so others will make a bracha for the zchus of the neshama) or other such actions that can positively affect the neshamos of those who have departed.
יש נוהגים לומר אזכרה למתים, וקרוביהם נודרים לצדקה לעילוי נשמתם, כי אף המתים צריכים כפרה, וכמו שאמרו בספרי, כפר לעמך ישראל אלו החיים, אשר פדית אלו המתים, מלמד שאף המתים צריכים כפרה
Some are accustomed to recite a memorial prayer for the deceased [on Yom HaKippurim], and those close to the deceased vow to give charity to elevate the deceased's souls; because, even the deceased need atonement as stated in [Midrash] Sifrei:
"Atone for your nation", these are the living; "whom you redeemed", these are the deceased. This teaches that the deceased need atonement.
Midrash Sifrei's Wikipedia article suggests that its section on Sefer Devarim was authored by Rabbi 'Aqiva or around his lifetime (Mishnaic/Tannaitic period).
איתא בתורת כהנים: כפר לעמך ישראל (שם כא:ח), אלו החיים. אשר פדית (שם), אלו המתים, מכאן שהחיים פודין את המתים. לכך אנו נוהגין להזכיר את המתים ביום הכיפורים ולפסוק עליהם צדקה.
It is found in Torat Kohanim: "Atone for your nation Israel", these are the living; "whom you redeemed", these are the deceased. From here, we learn that the living redeem the deceased. Therefore, we are accustomed to mention the deceased on Yom HaKippurim and to "[donate] charity on their behalf".
Midrash Tanhhuma's Wikipedia article, citing various sources, places its authorship at around 500-1000 C.E.
[...] The soul of a deceased person experiences great pleasure when his or her loved ones come to pray at [his or her] gravesite. These prayers provide immense benefit for the soul in the next world, thus prompting them to pray to G-d on behalf of the living.
Sefer Hasidim's Wikipedia article places its authorship "between the late 12th and early 13th centuries".