Depends if your experience/skills are in short demand here. The rule is Swiss/EU nationals first so non-EU are at the back of the queue and employers have to prove they can't find any of the former to do the job. https://www.sem.admin.ch/sem/en/home...zulassung.html
Yes, you could do a Masters here, but no you can't then drop the course as you'd come under exactly the same non-EU hiring rules. If you complete your Masters though then you'd have 6 months after graduating to try and find a job here while being on equal footing on the hiring front. https://www.sem.admin.ch/sem/en/home...abgaenger.html
There is a 4th option. Your girlfriend could apply for a concubine permit for you, but for this she would have to agree to be financially responsible for you for 5 years and I'm not sure you could work with that permit.
You need one of these options in place to be able to be here for more than the 3 months you're allowed as a tourist, otherwise you'll have to leave after that period for another 3 months before you can return here.