"will not precede" nullifies "at the same time"
"the dead in Christ rise FIRST" nullifies "at the same time"
"After that, we who are alive and remain are caught up" nullifies "at the same"
"the dead in Christ rise FIRST" nullifies "at the same time"
"After that, we who are alive and remain are caught up" nullifies "at the same"
This is saying that the "caught up" action FOR BOTH occurs "TOGETHER [ / at the same time]"
The outcome is (as the text states), "and so [/ in this manner] shall WE ever be WITH [G4862 - UNIONed-with] the Lord."
--the "WE" here speaking of BOTH who will be "caught up TOGETHER [/at the same time]"
--and this pertains to the "[TO] PRESENT - G3936" of the following two passages (pertaining to the SINGULAR "VIRGIN" / "BRIDE/WIFE"):
a) 2Cor11:2 - https://biblehub.com/interlinear/2_corinthians/11-2.htm
b) Eph5:27 - https://biblehub.com/text/ephesians/5-27.htm
... and none of those passages have taken place yet
(though I do agree that the "dead in Christ" are "ABSENT from the body" and are "present [/ at home with] with the Lord" even now... but the "G4862 UNIONed-with" thing awaits the "caught up" [all of us TOGETHER at the SAME TIME--at ONE SPECIFIC POINT IN TIME], to "IN THIS MANNER" shall we ever be "WITH [UNIONed-with] the Lord." But which point you are missing when you say some of the things you are saying in order to attempt to defend what you're saying...)
Now if you want to say that immediately after the resurrection the rapture will occur = AMEN