YouTube have a great way of indicating time in their URL for the videos. 
The Intent will look something like startActivity(new Intent(Intent.ACTION_VIEW, Uri.parse("https://www.youtube.com/watch?v=Z149x12sXs" + time))); where String time = "&t=0m30s";
Edit: Expansion for YouTube App.
public static void watchYoutubeVideo(String id, String time){
    Intent appIntent = new Intent(Intent.ACTION_VIEW, Uri.parse("vnd.youtube:" + id + time));
    Intent webIntent = new Intent(Intent.ACTION_VIEW,
                Uri.parse("https://www.youtube.com/watch?v=" + id + time));
    try {
        startActivity(appIntent);
    } catch (ActivityNotFoundException ex) {
        startActivity(webIntent);
    }
} 
Using another answer from that question. The same logic can be applied to any intent just add the Time string to the URI like shown above regardless of intention.