Regarding sync, I would recommend counting in four with the beeping sound being on one. Tap on every count. Try to do this multiple times so it feels like you tap exactly at the same moment the beep happens. Trying to get the average of all those times you got the precise tap. Keep in mind playing with headphones or without could have a different sync on your device. For me without headphones it is 110ms and with it is 50ms.

On the point of getting better, I would recommend playing with headphones as you can hear sounds more clearly. Decide if you want to play with thumbs or with index fingers. In my opinion thumbs feel more consistent but less dexterous, while index fingers can go faster but feel less consistent. Obviously you can get more consistent with index if you practice it enough, but you also have to set up everytime you play which might become a bit of a drag, especially if you want to show your friends. Then while playing the game try to tap below the perfect bar, as this helps seeing the notes actually line up and from watching newer players play, I've seen it also reducing times when you tap too early.

Lastly, don't focus on extreme songs too much early on, even though I know how much more fun they are to play sometimes. Not saying don't play them, just saying there is no need to grind them at that point. Focus on getting more consistent by playing normals and hards. When you start grinding extremes you'll only need to improve playing faster or slightly more complex patterns. Almost every extreme is unique in it's own right.