Geography and Migration
There are many interesting theories on how momo was introduced to Tibet, and most of them revolve around Han dynasty (ca. 206 BC- 220 AD) and Tang Dynasty (~ 700 AD). China has governed Tibetan territories many times in the past, which has led to considerable changes in Tibetan food and style of living, one of which is the introduction of momo (Majupuria, 1990). This infact, suggests that momo entered Tibet from China via the trade exchange that took place during silk route, which originally started in Han dynasty.
On the other hand, De Bao Xu, Professor of East Asian Languages & Literatures in Hamilton College predicts that momo entered into Tibet via the cultural exchanges that took place during marital ceremony during Tang dynasty, which is infact supported by some historical facts too- in order to maintain peace agreement between China and Tibet, emperor Zhongzong promised to have princess Jincheng marry with the son of the Tibetan king in 705 AD. After Tibetan king died, his seven-year-old son got enthroned. Then, another emperor named Ruizong from China sent Prince Jincheng to Tibet to marry the new Tibetan king together with a patch of land called Qiuqu in Hexi that lies at west of the Yellow River in China as a gift in 710 AD.
Likewise, there are there are image evidences suggesting the flourishing of diplomatic relationship between China and Tibet in Tang dynasty, in which emperor Taizong is giving an audience to Ludongzan the ambassador of Tibet Taizong (唐太宗) was a Prince of Qin. Taizong was a man of great contradiction in that he killed his two brothers and deposed his own father. Nevertheless, he proved himself to be a capable leader who listened to the advice of the wisest members of his council. However, after destroying a royal house of Jiali Khan, Taizong held a Buddhist memorial service for the casualties of war, he erected Buddhist monasteries at the sites of major battles so that monks could pray for the fall of both sides of the fight. And, it is during this process that he interacted with the ambassador of Tibet.
Last but not the least, the story of first radical 食 that I already mentioned in etymology section, was also established during three kingdoms period in China during Tang Dynasty. Thus, multiple evidences suggests that it was during Tang dynasty that momo was introduced to Tibet from China. Interestingly, Buddhism was introduced from Tibet to China during the same period.