Add an ExecStartPre statement to your service that calls a script that will not complete until the network is up to your satisfaction.
Depending on your configuration and needs you could loop until pinging an internet host is successful or check that your interface has a valid IP for your network. If having a physical connection is good enough for your needs have your script check the status of /sys/class/net//operstate.
You could also call such a script in it's own unit file and add it to the After statement in your service file.