Proposing research as Ph.D. thesis in Sweden
When it comes to PhD and postdoc positions there is essentially two types of positions, and some partially overlapping ones. The critical element here is where the money for the actual research is coming from. That is way more important than whatever idea you might have for a project. 

So if the money is coming from:


a specific grant with certain goals and deadlines, then the PI (the principle investigator, i.e. the group leader) will have to show some results. S/He will want to have someone work on that project and nothing else
alternatively if it's core funding (from the faculty/university/private funding etc) then the money is not "earmarked" and the PI can pursue interesting ideas more freely.


So assuming you are not bringing your own research funds, if you really want to work on your own idea from day 1, and not willing to compromise on that, then your only option is to find someone that has plenty of money and not many ideas. 

Not to sound too grim but you should know that it's a tall order