Nice job to you, from a 58 year old fellow mechanic. The kids could also use a socket of the exact same size to drive the race in. Toooo many videos from un-experienced RU-vidrs. This is the only way to correctly do this, brass punch was icing on the cake...lol
Most have a small depression, somewhere around the inside of the race to catch. If they don't have a recess cut, usually there is a small amount of bearing race that is catchable with a drift punch to get it started. I have had instances where a die grinder was used to create a small relief in one or two spots under the race to permit catching the race to drive it. :).