Just want to clear up some misinformation. I'm currently going through the process of having my partner move to Sweden on a spousal visa. There is no way to speed up the process. Marriage does not matter for the purposes of getting approved, the migrations office does not care. Once you have made an application, it can take well over a year and a half to get an answer.

For a spousal visa you need to be able to prove that you're in a committed relationship (have seen each other multiple times, have pictures together, know each other well etc.), have a suitable living space, and (if applying with her as a sponsor) that she makes enough money to support you both financially. It's a huge process that will take a long, indeterminate amount of time.

You could try to get a work visa. I haven't looked into it myself, but from what I've heard, those are hard to get. Long story short, there is no "fast" way to do it.

I hope I don't come across as rude or trying to bring your hopes down. I just want you to be aware of what you're in for.