There are a variety of centering cones out there, but all have a tapered area which mates to similar taper in the bearing or top cup. As long as it starts, it should slide in until it jams. In any case, it should never slide in all the way. The washers, spacers or trim parts have to sit on the cone which doesn't slide in far enough for the spacers to ouch the race.

If you can't get it started, it might be that the bearing is upside down. Remember taper fits taper.