I don't think so, I tried and I think there is no assistant-request event sent when starting a web call. What you can do is to init your vapi on client side using vapi sdk when you start the call, this way you can configure it from your codebase, but yeah that does not answer your need if you don't want to do it client side

vapi.start(
    assistant?: CreateAssistantDTO | string,
    assistantOverrides?: OverrideAssistantDTO,
    squad?: CreateSquadDTO | string,
  ): Promise<Call | null>;