How many creations are in your Sporepedia (under Everything)?
If you leave the game on the black screen for a few minutes, does the game eventually load? Don't click on anything or press any keys, just wait and see if the EA logo comes up and the game starts.
Some systems can take a long time to load the creation database when the game starts. This issue can be especially noticeable if you have a lot of creations downloaded (especially over 8-10k). The game is not frozen, it is simply taking a long time to load.
Load times can be improved by reducing the number of downloaded creations. I've found that fast CPUs and SSDs help, but I know it's not feasible for many people to upgrade their computers.
However, it's also possible that there is actually something wrong with the game. If you have a fast computer (fairly recent CPU and an SSD), don't have many creations, or the game crashes even when you don't do anything, that would be an indication there's something else wrong. In that case, I would suggest reinstalling the game to start. If it still doesn't work after that, respond back, and I'll get some more info from you.