i want this to sound smooth
At first I didn’t believe that I could relate to my classmates in any way; we were all unique in terms of backgrounds and social classes.
It's all in 1st person, but see if you like this any better:
At first I didn’t believe that I could relate to my classmates in any way: Each of us is unique in terms of backgrounds and social classes.
You could substitute "because" for the semi-colon.
To make this sentence sound smooth, we can make a few adjustments while maintaining the original meaning. Here's a revised version:
"Initially, I had doubts about finding common ground with my classmates due to our diverse backgrounds and varying social classes."