The Mishkan of Nov began in Year 2871, from the day Eli died. Even though there was an Ark of HaShem in Kiryat Yearim, they would offer sacrifices in Nov for 12 years until Shaul died [(Seder Olam, chapter 12) (Tzemach David). And in Tractate Zevachim: the altars - from when they entered the land, they erected the Mishkan in Gilgal for 25 years, and from there they brought the Ark to Shilo, and it stood there for 369 years between stones below and curtains above.
When Eli died, Nov was destroyed and they came to Givon (see Year 2895), and from there they came to the eternal house. It stood in Nov and Givon for 57 years. And from that day forward, all places were forbidden for offering sacrifices except in the Chosen House. (And this requires investigation, for they entered in Year 2489, and the Mishkan stood in Gilgal for 25 years and in Shilo for 369 years until the Mishkan of Nov - that would be Year 2882, so how did he write that the Mishkan of Nov began in Year 2871?)].