So you just want a better system than “completely at random”. Fair enough. Here’s what I’d do:

1. After the first line is uttered, see if the subtitles are late or early. Pause.
2. Adjust the delay, let’s say -1.0 second (or more if the difference between them felt really long).
3. Skip back to before the line was heard, and play. Is the gap better or worse? If it’s worse, then you need to change the delay in the other direction (+1.0 instead of -1.0). If it’s better, the direction you used was good.
4. Repeat step 3 until you get that one line synced perfectly.
5. Enjoy the rest of the movie/episode.

Disclaimer: I’ve never had this problem (that I remember), subtitles have always been either synced or completely out of my control. I don’t use ‘alternative means’ much.