They have already been setting up an influence with how they are lying/misdirecting Elrond and Galadriel. There is the blight as well. However they can easily forge the rings first 16 at the end and explore what you say when Celebrimbor forges his rings in Season 2. There was 90 years between between the first 16 and the next 3 greater rings. Another 10 years for the One Ring.
So Season 2 can open with the betrayal and cover the War. Season 3-4 cover the creation of the ring wraiths and Season 5 will obviously be the War of the Last Alliance.