Basically, you don't need a startup clearance at all...
The general purpose of the startup clearance is to validate and activate your flightplan. If you want to start your engines and burn fuel before you know your fpl is approved, go ahead.
Having said that, there are other considerations:
1. Noise - Some airports forbid having running engines or APUs. Some specify you can start it up 5 minutes before pushback. Check your local procedures.
2. Safety - Having an engine on is a safety issue, and your airline should publish procedures to handle that, beacon, ropes, cones, whatever. Some airports also have their special rules about that.