How to get the exact current timecode? - or - How to integrate your subtitles into someone else's video on YouTube?

Question

YouTube

I am making an extension for YouTube that will show subtitles not in two lines, but in one word. As it turned out, YouTube stores automatic subtitles in an xml file where the exact timecodes of each word are indicated up to a millisecond, and which can be obtained simply by turning on subtitles. Now the question is how to get the exact current timecode so that you know exactly when to output which word? YouTube gets this value from somewhere. Please tell me in which direction to move?