Not without going through Russia. There is no longer any passenger train connection between Finland and Sweden, so that would require either going through Saint Petersburg or crossing the Baltic by ship. You can however do the trip by car; it's just going to cost _a lot_.
I'm now living in Berlin instead of Helsinki, and I take trains to go pretty much everywhere in Europe. When you factor in the time of getting from/to airport, security checks etc. it is often nearly as fast and much more comfortable. As I write this, I'm having lunch near the railway station before leaving for a conference in France. Usually I'd eat in the train but now I happened to have the time to spare...