Just purchased a new Savage A22 WMR and will not shoot Winchester ammo looks to me like firing pin is not hitting hard enough I have heard that winchester case's are harder anyone have any experience with this.
Shouldn't matter about the ammo casing being harder. The gun should hit it hard enough for ignition. If it's a new gun as you stated, I would take it back to the store you purchased from and let them make it good.
I have had a lot of trouble with Winchester white box. They swell so bad that I have to dig them out of my .22 rifle with a knife. Their white box shotgun shells also swell so bad they have to be dug out of my single shot. They have really lowered their quality control. I would try different shells before anything . Its not every brick....but enough that its a pain. My Ruger American Rimfire will not feed a lot of Remington shells for some reason, but will any other. Good luck.
Case dimensions and bullet profile can cause issues; Check 2 things:
1] bump the bolt closed with your hand after loading [like the fwd assist on an AR.] Some rounds go in just far enough so the gun will fire [in battery] but the pin just pushes the cartridge forward the last little bit.
2] load and eject an unfired round, see if it ejects easily and if you can see any marks on the bullet where it may be contacting the rifling. This can result in  above, the pin pushes the case forward robbing it of energy needed to pop the primer.
2(a)] With bolt open try hand loading a round, push in with a flexible coffee stirrer / popcicle stick etc. See if you can fully seat the rim without excess force. Then see if you can extract easily with a thin strip of plastic cut from a gift card or similar 'thinner than a credit card' piece. [Clear 'clamshell' packaging works well for this if not too thick.] Idea is to make sure the cartridge is fully seated and cannot move fwd when hit.
If none of these then try to measure rim thickness of good/bad ammo. This can vary.
It could be an issue with firing pin protrusion and/or headspace but if CCI / Remmy ammo works fine I suspect its something in that specific Win case/bullet.