According to The Hashtag Show, The Eternals is tentatively slated to begin filming in September 2019:
“The Chloe Zhao-helmed film which Marvel Studios hopes will kick off a new franchise is tentatively scheduled to go into production in September of 2019. That start date puts the film on track for a November 6, 2020 release, right where we told you to expect it.”
In a follow up Tweet, they said the movie is “on the books” for a September 2019 start:
I know when we ran the 2020 slate piece a lot of you did not think Eternals was going to be moved into that slot. This info is from a different source who says they have put it on the books to start production September 2019.
— Charles Murphy (@CharlesMurphTHS) November 6, 2018
If does end up happening, it does mean that The Eternals looks a lot like the November 6, 2020 movie. It’ll be interesting to see how they handle the characters’ introductions in the MCU as they were originally rumored to be intro’d in Guardians of the Galaxy Vol. 3.