In a fascinating thought experiment, the article explores the possibility of advanced civilizations on Proxima b, a planet in the habitable zone of Proxima Centauri, having sent spacecraft to Earth with increasingly advanced propulsion technologies. It discusses how these spacecraft, starting from chemical rockets a hundred millennia ago, could have arrived at different points in Earth's history, eventually leading to the concept of 'archaeology of interstellar propulsion.' The article suggests a timeline where hydrogen-propelled spacecraft, light-sails, and nuclear spacecraft could have reached Earth thousands to tens of thousands of years before the present time, challenging traditional views on interstellar travel. The hypothetical scenario presented in the article implies a continuous improvement in spacecraft speed on Proxima b, with implications for the potential impact on human development if such advanced technologies had visited Earth in the past. It raises questions about the history of propulsion technologies and the possibility of detecting traces of these technologies on Earth. The article concludes by proposing that biologists may find anomalies in human DNA if human intelligence was influenced by such visits. Furthermore, the article touches on the concept of an interstellar exodus from Proxima b to Earth, drawing parallels to historical migrations. It speculates on how the timing of departure and the advancement in propulsion technologies could influence the arrival times of migrants. This thought experiment challenges existing notions of space exploration and opens up new avenues for interdisciplinary research in archaeology and astronomy.