I purchased a CZ in .375 H&H Magnum a few months ago. I have been hunting with centerfire rifles such as .308's & 30-06's for over 30 years & I wasn't too concerned by the recoil, but I also wouldn't recommend a .375 H&H for a beginner.
I have used a .375 H&H in Africa on plains game on past hunting trips. The rifles I used in Africa were a heavy Barrel Remington, which didn't kick much at all due to its weight, & a Whitworth Interarms .375 H&H that was fitted with a muzzle brake. I didn't like the deafening blast associated with the muzzle brake, & definately preferred the heavier rifle for shooting.
I mainly bought the CZ for use in controlling feral goats & pigs on my 3,500 acres. I also own a number of other firearms, but there is something satisfying firing 300 grain bullets around the countryside.
First day at the range, I put 40 rounds of factory ammo through the .375 off the bench, & I felt it the next day. Since then I've mainly hunted with it, & from field positions I don't fee the recoil.(much)
I haven't yet taken my .375 out to the mountains where I hunt deer, but I will be. I'll probably still take my Sako .308 & just use the .375 occassionally for hunting in the mountains, as one disadvantage of the .375 in the weight of the rifle. That said, I would still rather have a heavier .375 H&H that I enjoy shooting, rather than a lightweight .375 that would lead to flinching.