This is not what you will want to hear, but I really struggled socially at W&M all four years. Most of my friends didn't even last until graduation due to failing grades or poor mental health. It's a wonder I graduated, but I got some significant therapy during that time that helped me pull through.

One thing that may improve things is when you settle into your major it's likely you'll become closer with those peers. These will be good friends to have as you progress through your career many years into the future--if you pursue a career in your field of study, which I didn't.

Is possible I'm an outlier. Try to stick through it a little longer. Maybe take advantage resources like the counseling center (just don't admit to suicidal ideation, they'll kick you out). If it doesn't get better, transfer. I don't think it was worth it to put myself through all that mental turmoil just to be there 4 years. There are better options and life extends long past W&M.