3 ideas
Require every guest to wear a name tag with their first name written large enough to read across a room. This removes the cognitive burden of recalling names, lowers the social friction of approaching strangers, and signals that the event is designed for mixing rather than clustering with people you already know.
A host-led icebreaker where each guest answers a single prompt aloud to the whole group converts a room of isolated conversations into a shared experience and gives everyone a reason to approach each other afterward. The structure does the social work that shy guests cannot do for themselves, manufacturing the warmth that would otherwise depend on luck.
Hosting a deliberate gathering of 15-20 people you barely know builds your network more efficiently than attending others' events, because the host occupies a position of authority and gratitude that accelerates trust. The act of inviting and convening makes you memorable and central in a way that being a guest never does.