Here are a handful of songs from the 80s that sound to me like the 90s.

The Sugarcubes: Motorcrash (1988)
I can't listen to long stretches of Bjork. But I need at least one song a day. Like a vitamin. And while "Birthday" was the best preview of Bjork's solo career, Motorcrash feels most to me like a 90s song trapped in the 80s.
https://www.youtube.com/watch?v=vz9WNOkVTWo

The Wonder Stuff: Don't Let Me Down, Gently (1989)
"A Wish Away" was the first hint of things to come (and still my favorite by this band), but its chorus could have been sung any time in the 80s. "Don't Let Me Down" has made the transition.
https://www.youtube.com/watch?v=SIKUZjc4gVo

Dramarama: Anything, Anything (I'll Give You) (1985)
Power pop may be timeless, but to me this song forecasts the pop punk of the 90s. Although it's unabashedly earnest, so perhaps it's forecasting emo.
https://www.youtube.com/watch?v=Azj_AjdNWwY

Pailhead: I Will Refuse (1988)
If Dramarama forecasts 90s pop punk, Pailhead forecasts 90s hardcore and industrial. An interesting collaboration between Al Jourgensen, who was transitioning Ministry from synthpop to industrial, and Ian MacKaye, who had Minor Threat behind him and Fugazi ahead of him.
https://www.youtube.com/watch?v=kUHsBuCKSdI

Faith No More: Falling to Pieces (1989)
I debated putting RHCP here wink wink. But The Real Thing is a perfect album. It has everything, from the growling speed of "Surprise! You're Dead!" to the MTV-fodder "Epic" to the funky bassline of "The Morning After" to the best-yet cover of Black Sabbath's "War Pigs." You can make whatever arguments you want about grunge defining the 90s, but for me it was The Real Thing that marked the turning of the decade.
https://www.youtube.com/watch?v=32bdevGClD4