So, there is a lathe-bored recess in the sprocket, which is also the drum drive clutch, and the outer ring of the bearing which supports those parts is intended to fit into that recess?
First, be very sure there is no raised burr on the entry to the sprocket recess. It is usual to run a file or deburring tool around the corner surface first. Clean the bore, and the outer ring of the bearing. The insertion would normally be made by using a press, which holds the parts square and pushes in a very controlled way. There will not be much force involved when you get the parts clean, square to each other, and burr-free. It isn't possible to use much force because you are necessarily fitting the outer ring of a ballrace into a housing by pushing on the inner ring - a process that would turn the bearing manufacturer apopletic, but is probably the only way it can be done in this case.
If you have a decent-sized bench vice, it will make a good substitute for a press, both in holding the parts square and applying all the force you need (with a great deal to spare). The worst thing to use is a metal hammer, since it brinells both races of the bearing. A rubber hammer is acceptable for applying force, but it does nothing to help you get the parts square.
