Unless your built like Barney Fyffe then shooting that 375 should not be too bad as long as shooting a handful of shots. If you need to shoot more than that definitely get or borrow a lead sled to sight it in. Felt recoil is cumulative and just target shooting can cause a development of a flinch, then your just working against yourself. Most rifle I have ever shot is 30-06 with 180 grain and even just target shooting with that after about 7 or 8 shots, you really have to focus. Right now the only rifle I have is 270 WSM. It only kicks about like a 20 gauge but man that gun shoots flat.
BTW you definitely, for posterity, need to film you shooting it. Btw I am pretty certain that .375 will kick less than the nitro express gun seen below.
https://www.youtube.com/watch?v=4Yj4IL0Q754
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