For this exact reason I started all my children with a cork gun bought at Dollywood. I used it to teach them safety(muzzle direction) , but also it was quiet and did not kick, because a “ trigger pull flinch” is very hard to un-learn. I slowly graduated each of them to Daisy Red-Rider BB guns. Then to Marlin 39 a from a bench , so the could work on target acquisition. Plus a subsonic 22lr from that heavier 24 inch barrel is really quiet and still no kick. Eventually as they got bigger and older we moved on to 22mag then our first center fire was 38 from you guessed it a 20 inch barrel Lever gun. Then 357 from that same lever gun.
Now all this was a slow progression, but my kids never developed a “trigger pull flinch” . All of this was important to me , because at 7 years old my dumbass older brother thought that making me shoot 3 inch magnums from a 12 gauge would “ mak-uh man out of yuh”
. What it did besides give bruise up side the right side of my head was give me a flinch that took me years to un-learn.
I am currently using the same process with my grandchildren. Your mileage may very , but the 22lr or is still my favorite cartridge