How is that possible if Rapture and Columbia never exist in the same reality
The same way Fink and Suchong and the Lutece Twins are in the same reality, even though they are from different ones...
AND Elizabeth's doings prevented it from ever existing in the first place after Infinite's ending?
I think you didnt really follow the end of the game and Burial at Sea. Elizabeth tried to break the cycle at the end of Infinity, but as we can see in Burial at Sea 1, it didnt work for all timelines since Comstock got "created" also through other ways than just Bookers Baptism at Wounded Knee.
There's only one Existing Columbia and that's the OG one that still needs to exist due to its actions having repercussions in Rapture's reality
There are millions of Raptures, Columbias and other cities that arent specified so far.
"There is always a man, always a girl, always a lighthouse and always a city."
Gentleman would've to be some kind of inter-dimensional thingy from Infinite's reality and I don't know how they'd explain that, nor why would they go with that overcomplicated route to begin with.
See my first point.
Elizabeth is long gone so Tears wouldn't exist, either.
Elizabeth isnt the source of the tears, as can be seen with the Luteces creating tears to actually get Elizabeth from another dimension.
Elizabeth got her powers from being pulled through a tear while being an infant, not the other way around.
I mean, even if Columbia did exist in Rapture's reality, most of the scientists would be super dead at the time (Infinite's 1912 setting vs. the supposed 1971 of this one), how would they be able to create that?
The cities cant and wont exist in the same reality, different universes/realities again.
As it seems common, you and many others really missed a LOT from the story and came to completely skewed conclusions.
You can check everything i said directly on the wiki if you dont believe me. I mean you could have done that in the first place before commenting and would have answered all your questions that way too.