In the original game, there's a visual cue that lets you know when you should skip the intro in order to get the speed glitch. According to the speedrun guide to the original game:

At the Lucafilm Games logo, Press ESC when you see the very first "sparkle" on the L, as long as you skipped once sparkles start happening then you will have the glitch.

Other than the visual cue, there's also an audio cue: at the same time the logo starts sparkling, there's a flurry of four notes.

In the Special Edition, we don't have a sparkling logo, but we still get the flurry of four notes! Pressing Backspace to skip the scene at that point will get you the speed glitch.

There's also a visual cue: at the same time you hear that flurry of four notes, the text "Deep In The Caribbean" appears on the screen.

If you're using the new graphics, you'll notice whether the speed glitch worked almost immediately because, if it worked, Guybrush will be able to get closer to the edge of the screen while he's walking to the scumm bar. That doesn't happen with the classic graphics, though, so knowing whether the glitch worked is a bit harder. In any case, you've got plenty of time to press the Backspace key, so once you get it once, you'll be able to get the glitch almost every time.

The getting the speed glitch video shows the results.