If you can make it on to the local train from Aachen to Welkenraedt, change to a Belgian IC train. The fastest connection to Antwerp goes vis Leuven (no need to go via Brussels). Those are hourly trains that don't require a reservation.
If you can make it to Liège or Brussels-Nord that's a bonus. Brussels to Antwerp has tons of trains, like a suburban service basically. Just get on the next available.