Can I hit the ball before it bounces on my side?

Not if it is still over, or heading towards, your half of the table. That is an obstruction and you lose the point (Laws 2.5.8 and 2.10.1.6).

You obstruct the ball if you, or anything you wear or carry, touch it in play when it is above or travelling towards the playing surface and has not touched your court since your opponent hit it.

If the ball has already passed beyond your end line (the end line counts as extending indefinitely sideways) or is travelling away from the table without touching your court, catching or hitting it is not an obstruction: your opponent loses the point because their shot missed your court (Law 2.10.1.4).

Note that the ball touching your racket hand below the wrist counts as a stroke (Law 2.5.7), so a return off your fingers is legal.