Well... yes and no. Mostly no. Let me explain.
"Random" textures in Minecraft aren't truly random. Nothing in computers ever truly is unless there's an outside analogue source determining the outcome. In the case of Minecraft, the game uses the coordinates of every block in the world to determine its random texture. If you place a block down, pick it back up, and put it back in the same space it'll always have that same "random" texture.
In this way you can trial-and-error getting one specific random texture for a single block space in the entire world. Yes... in the ENTIRE WORLD. Because once you get one specific coordinate to be what you want then you've lost control over the rest of the blocks to get there. And even this could take a long time depending on how many variants you have, and how rare they are. So it's not really a good solution for the vast majority of applications.
Now you're probably thinking that this isn't really what you wanted to do. You wanted to just be able to write your XYZ values in a file and call it a day. Understandable. But sadly, no, that's not a thing. If you want that you're going to have to use a different block entirely in order to get that space filled with precisely what you want it to be filled with. Chances are there's at least one block in the entire game that you're not using much of that you can retexture. (Maybe the Birch Wood block? Not to be confused with Birch Log or Birch Planks.)
Sorry to be the bearer of bad news, but I hope that helps you.