Yep, it occurred to folks several thousand years ago. The first coins were made just that way. But you'll be limited in the quality of image you'll be able to produce.
Making a die isn't easy. To stand up to repeated use, it will need to be made from steel and heat treated when it's finished.
To make even a small coin, you'll need a serious press. Think around 100 tons to start.
If you can make the dies and have the press, you'd be able to make consistent weights by pouring an ingot, rolling it to thickness, then punching out blanks.
You can try making a die and whacking it with a big sledge hammer, but again, the lack of control over that process will affect your ability to produce quality results.
I'm not trying to discourage you. If you're successful, there are many here who would probably like to follow your example. There are a few threads on the forum about making coins.
Dave