I think this package does exactly what you need: https://pkg.go.dev/github.com/google/gopacket/routing. Works on my machine (error handling left to the reader)

    router, _ := routing.New()
    iface, _, _, _ := router.Route(net.ParseIP("8.8.8.8"))
    fmt.Println(iface.Name)

this prints my Ethernet interface as expected. It doesn't make any requests, it just figures out where to route a packet. I guess it interfaces with the OS routing table.