Can I write a scientific paper with just the ideas? Without any mathematical proof. I plan on writing about the origin of the universe.
Define 'scientific paper'.
Of course you can write a paper if you want. The question is, what do you want to do with it?
Submit it to a peer-reviewed journal? No.
I do wish to publish my paper to a scientific journal, will it not get through if I don't have a supporting data?
Of course not. It's not science without data.
You would be better served by reading journals than worrying about writing in one. Scientific publication is a dialog, and wanting to write without reading is the same as trying to have a conversation by talking and not listening.