The green tint was not part of the original theatrical release. The green tint was used in the sequels and then added back to the DVD/Blu Ray release of the original movie.
You can go on Youtube and watch trailers for the original theatrical release and compare them to clips posted from later DVD releases. For example here is a comparison of the original theatrical trailer to a fan made trailer using clips off of the DVD using the infamous "Guns... lots of guns..." scene:
https://youtu.be/tGgCqGm_6Hs?t=91
To this:
https://youtu.be/atqOCj3qzzA?t=110
You can compare other scenes as well, it's clear the original film had no green tint and in fact I personally like it better without the tint.