or_iginal, it only took a few moments before the Falcon's full engine 'glow' appeared in that SE addition in 'ANH', as it rose upwards. We saw the rear 'detail' for a short time, but overall it was fully 'glowing' pretty quickly after lifting off.

As far as the 'platform' take-off, there was plenty of time for it to have been fully 'aglow' from when Chewie sits down to charge up the engines (C3PO gets dragged by R2, and then we see Stormtroopers firing in-between times), to when we see it lift off the platform. Also, it's almost facing us as we first see it turn around as it takes off from the platform, so this all makes it consistent with being fully 'aglow' by the time we see the rear of it.

The sound effect just seems to tie-in with when the Falcon zooms off straight ahead, after it has lifted up and fully turned. Although the engines are already fully 'aglow' at this point, it works fine for me I have to say. I think you could be right about that sound effect in the trailer not being audible in the official release, perhaps due to the crescendo of the music at this point.