Half a mm sounds like a lot too much; something is wrong in a big way. It's time to (relatively) accurately measure ID of the head tube, and OD of the headset to work out which bit is not what it's supposed to be.
If you try forcing it in, you'll break one, the other, or both. A "press fit" is H7/p6, which is to say that the "hole" should be on nominal diameter or up to 25 microns oversize, the "shaft" should be between 26 and 42 microns over nominal diameter for that diameter range- that's ~1/20mm *maximum* difference, or "just about discernible with a decent set of vernier calipers* if you're lucky, you really need a (very) expensive micron-level micrometer to get a decent reading". If you can see the size difference, something is wrong.
* yeah, chinese electronic calipers claim 1/100mm resolution, but their jaws can be off spec by over 1/10mm...