Unable to find correct tire size
Those appear to be hooked rims,(difficult to see in the pic) which are almost all iso-622. iso-630 rims are usually straight sided rims and used only on 25-50 year old road bikes. Occasionally tires are just made with tighter bead wires. You must fully deflate the tire and break the bead seal all the way around on both sides so that the edges farthest from where you are working can slip into the center well without resistance.

You should not expect to put the first bead on fully without levers, it does happen occasionally but don't expect it. Technique is a big thing but I can't help you with that without being there.I have done some ten thousand bike tires in the shop, manufacturing tolerances are quite wide, not much you can really do about it other than practice.On the plus side, tight bead wires are less likely to let the bead pop out and cause the tube to blow out, which can happen if the tire is near max pressure in the cold morning and then parked directly in the afternoon sun. It sounds about like an M-80.