NoNewTask.cs

static async void Main(string[] args)
{
	Func<Task> startupDone = async () =>
	{
	    await Task.CompletedTask;
	};
	
	var taskHere = startupDone.Invoke();
	var runTask = DoStuff(() =>
	{
	    taskHere.Start();
	});
	// Here we wait for the task to finish.  Or timeout.
	var didStartup = taskHere.Wait(1000);

	Console.WriteLine(!didStartup ? "Startup Timed Out" : "Startup Finished");

	await runTask;

	Console.Read();
}

public static async Task DoStuff(Action action)
{
	// Swap to 1000 to simulate starting up blocking
	var blocking = 1; //1000;
	await Task.Delay(500 + blocking);
	action();
	// Do the rest of the stuff...
	await Task.Delay(1000);
}