I press the hammer on the tumbler by thumb to get it well started. Then I place the hammer flat down on a bench block with something non-marring in between. I use paper towels. Then I use a brass hammer, one pound is fine, to tap the tumbler into the hammer. Patience rather than big whacks is better. Go straight and check to make sure it is going straight. You don't want to accidentally distort the square hole in the hammer.
You can also press it on using the jaws of a vise, again protecting the finish of the hammer. But I prefer tapping it on. YMMV.
Locks as they come from the manufacturer often do not have the hammer all the way seated. How far you want it is your decision. I do not like a huge gap between the hammer and the lock plate. You might find that you need to shorten the square section of the tumbler, or even migrate it, to get the gap you would like to have whatever that might be. I like the square shaft to come to just a hair short of flush with the surface of the hammer, for maximum engagement.
More seated is more solid. Fully seated is most solid. But if you get slop, fully seated gives you nowhere to go so then you need to tighten up the hole in the hammer, which you can do.
If you have slop where the tumbler can move in-out more than a hair when the bridle is installed but not the rest of the mechanism, you either need to fix that or make sure the hammer can clear the side of the lock plate and any protruding screw tips no matter how the tumbler settles in. I've seen enough slop that a fly could potentially get jammed in the gap! That's the point where you HAVE to fix it!
Others may give you other advise. Listen to them!
Gerald