Edge routers are usually (AFAIK) used as a solution to protecting incoming DDOS attacks.
To prevent internal clients "unknowingly participating" in an outbound attack, - I'd consider what ways a DDOS might "involve" your clients.
For example, holes in WordPress are often used; so if your clients are webservers running WordPress, keep them patched (and/or a WAF in front of them). Make sure your security policies are sensible, maintained and enforced - I've seen way too many boxes compromised and silently used as parts of DDOS attacks. File integrity monitoring is sensible, and regular (even better automated!) monitoring of system user accounts etc.
If your clients are desktop/laptops, then antivirus and sane (local) firewall rules are an obvious start, plus blocking anything insane things at your core switching layer (broadcast is often necessary for a wide variety of things and likely even part of a DDOS - they're usually targeted ["uni"cast], but does your network really need to pass UDP traffic > port 1000? Or ICMP packets with a large payload or at a rate > 10 a second per port?) will help.
User training and restriction is sensible too - who's got access to these devices? Are they allowed to install whatever they want from wherever they want?
Finally, just a little sane monitoring of network throughput. We use Zabbix, but there's a ton of choices out there. I've caught more than one outbound DDOS attempt due to a sudden unexplained spike in the network I/O... A little care in setting up alerts when things go way outside what you deem "normal" for a prolonged period of time is seldom a bad idea.