In a previous life, I dealt a lot with fracture mechanics of bone. How fractures occur in bone can depend on the ossification of the bone (the more solid, the more cracks can show), uniformity (bone is pretty good at being uniform, but far from perfect), type of bone (not frontal, parietal, or femur, but compact/cortical or cancellous), and condition of the bone as fresh (still containing collagen as when alive) or dry (without collagen). If a .22 caliber bullet left a 2 cm entry wound in a skull, not in the soft tissue, but in the skull, I would say it is an absolute possibility. Radiating and concentric fractures from/around the point of impact could most definitely result in a hole through the skull that is larger than the caliber of bullet, particularly if off of the soft tissue has been removed before examination.
I would not anticipate finding a person who had been shot in the head with a .22, even at close range, to have a gaping 3/4" gaping hole through skin, bone, etc. The exception, would be angled shots and those certainly do occur and on a round surface like a human skull, it can be hard to make shots perpendicular to all of the immediately surrounding tissue.
Approximately 2cm is approximately 3/4 inch, and so impact angle, matters. Where on the skull the wound is, matters, the skull is not a uniform thickness. Thin bone might shatter, leaving a larger wound than thick bone where the wound might just be a bullet size hole, etc...
Generally speaking, the skull is composed of an inner table of then compact bone, diploe or cancellous bone (which is porous, involved in blood production) and then the outer table that is usually another thin layer of compact bone, sometimes thicker than the inner table bone and sometimes not.
Compact bone and cancellous bones have different fracture patterns due to the gross structure of the bone itself, cancellous being porous like a sponge and compact bone being a solid (though not a uniform solid). One of my students compared it to two layers of drywall with sprayed foam inside and that isn't a bad visual analogy. When thick enough, compact bone can be broken very similarly to rock like chert. It has predictable and documented fracture dynamics, though for a flintknapper, it needs to be thick enough to work with and that isn't the issue here, although it would not be.
As such, bullet wounds to the head can produce the original entry hole that is about the diameter of the bullet if it goes in perpendicularly to the entry surface. That hole would be on the outer table of the skull. Where the bullet impacted would have radiating from it all of the energy of the bullet that the bullet can transfer equal to the resistance of the bone and soft tissue. From the point of impact into the skull, the energy is going to dissipate in a cone (Hertzian cone, or cone of percussion). If you have ever shot a plate glass window with a BB gun and seen funnel-shaped hole left behind, that was a cone of percussion. Given that the layers of the skull likely would not be uniform, this cone is not always uniform, either. While the hole through the outer table may be bullet diameter, much of the diploe and inner table may be missing from under the outer table to a much greater diameter. If there are associated radiating fractures and concentric fractures, the outer table which would otherwise show a bullet caliber diameter hole may end up having a much larger and likely less regular (in shape) hole, but to really notice it, all the skin would need to be gone from the area. I think 44 Amp referred to this as the skull shattering, but it would not be shattering like a window, but simply having structure failure around the point of impact, that structural failure being much more pronounced on the inside as a result of a cone of percussion.
Otherwise, no, I would not
expect your typical .22 (lr, short, long) to produce anything resembling a typical bullet entry entry that is 0.75 caliber in a human skull.
With that said, expectations are not always what greet us in the field. Human/animal tissue may tend to perform in certain manners when impacted by ballistic projectiles. What bullets tend to do going through soft and hard tissue is far from uniform, however, as the hard and soft tissue are hardly uniform across the body or from person to person. For example, you may see much greater destruction than would be expected if you are shooting an 80 year old in the head who has failing health versus a 30 year old in the head who is in peak health.
So yeah, if I was to give it a number, I would say 4. If the hole was that big, I am sure there is a good explanation for it.
Of course, there was the about about a "few inches" distance. I am not sure how far that is, but when it comes to gasses and their impact, very minute amounts of distance makes a difference. If by a few inches the op means 4-8" then I would say that gasses are not apt to influence the wound an any significant structural manner, particularly through the bone. If 'few' is >1 and <3, then maybe.
(.787xxxxx) according to my calculator.