Make sure the C-ring opening is
DOWN. Notice the ring is a bit oblong. it protrude from its channel on the sides (if you call the opening "top" or "bottom"). Hold the axle with the opening up and you'll see that it hangs down and will also protrude from that opposite end. If you insert the end with the clip/ring opening down, gravity is helping to keep it from protruding and presenting an obstruction to installation. Also, don't even mess with using a hammer and block, or chisel, or whatever on those flat spots on the inner housing.
Insert it carefully until it stops at that ring. Then, keep some inward pressure and use the flex in the inner boot to tap it in using, basically, the end of the axle where the tripod bearings are (inside the inner boot). You won't cause any damage. You don't even have enough travel in the boot to generate much force. You're just tapping. It should only take a few taps and it'll pop right in. Just make sure that C-ring has the opening facing down. I just changed my CV's last month. It was so easy. here's a video where they install the axle the same way:
https://www.youtube.com/watch?v=hHY1rpRD11g
UrbanRunner651 said have someone tap on the outer end of the shaft. That will work too. Make sure to use a block of wood so the metal doesn't get marred (or use a dead blow with the plastic coating). And make sure, when holding the axle, you keep it level and keep slight inward pressure.
Incidentally, when you're removing an axle, they can be a PIA to pop out of there for the same reason. In my recent swap, I was bashing on a chisel to get one out, and I happened to rest my arm a second and I rotated the axle a little. I must have rotated it to where that ring was oriented open side down, because the next hit was not very hard and It popped free. It won't pop all the way out, but You'll see clearly that its free from it's fully seated position. Anyway, just a few thoughts on these pesky axles.