https://stackoverflow.com/a/73535590/1271826

MultipleRandomTasksAwaitFirst.swift

actor Foo {
    private var firstTask: Task<Void, Error>?
    
    func performFirstTask() async throws {
        // create unstructured concurrency
        
        let task = Task {
            try await …                         // the work associated with first task
        }
        
        // save this task for future reference by other functions
        
        firstTask = task
        
        // because this is unstructured concurrency, we need to handle cancelation manually
        
        try await withTaskCancellationHandler { 
            try await task.value
        } onCancel: { 
            task.cancel()
        }
    }
    
    private func startOrAwaitFirstTask() async throws {
        if let firstTask {                      // see if first task has been started …
            try await firstTask.value           // … if so, await it
        } else {
            try await performFirstTask()        // … if not, start it          
        }
    }
    
    func performSecondTask() async throws {
        try await startOrAwaitFirstTask()        
        try await …                             // the work associated with second task
    }
    
    func performThirdTask() async throws {
        try await startOrAwaitFirstTask()
        try await …                             // the work associated with third task
    }
}

By the way, note the use of actor to avoid race on firstTask. Alternatively, you could make foo a Sendable type, e.g., a class isolated to some global actor. But you want to avoid races amongst these three tasks.