Use STN probably about 50 times a year and I personally woildn't be happy with so little time.

From train station it will take you about 5 min to reach security. 05:44

At that time of morning queues can be anything from walking straight through to 15-20 minutes 06:04

If your a/c is parked furthest away from the security you then need another 15 minutes to the gate. That means you could be at the gate at 06:20.
If you are the last one and on HBO they will likely close the gate at -20 (definitely will at -10) . So you are leaving yourself only 10 minutes of buffer time which is way too little for me. Obviously everyone is different.and for some this would be enough.

I would much rather get 04:28 bus 510 that gets you there about 04:45 giving you quite a bit of extra time but much more comfortable.

I personally arrive about 1.5 hrs before and that gives me a plenty of time to stroll to the gate and stop.on the way in Pret.