Let me tell you just what the TTGL can do. It can swing its galaxy sized arm so much faster than lightspeed that, if you think in worldlines, it can instantly punch any point in the galaxy. But that's not all! Its hand is actually about the size of the central cloud of the galaxy, so it will seriously twist worldlines around it. The net result is that the TTGL can (probably, depends on how heavy it is) punch things in the past, before they ever started moving. It could also send a massive black hole into the past by detaching its hand, thus removing the spiral power that keeps it from collapsing.
Or it could just take whatever galaxy the Flash is in and crush it instantly - every star would move towards each other at over lightspeed so you couldn't even tell he was doing it from anything other than massive blueshift in the sky.