I am thinking of doing a PhD. Problem is, I am not a student and the only professors I do know are the ones from the university I took my bachelor and Master's degree. However I was thinking of changing institution or even moving to a relevant scientific field and thus I do not want to contact one of those professors. I have located some institutions and faculties I might be interested in following a doctoral programme. Question is how can I contact one of the faculty professors, since I do not know them either personally or academically? Is there any other way except of spam emailing them?
The difference between "spamming", which you should not do, and a completely acceptable contact is how targeted your emails are. Make sure you know what you want and what the professor you are contacting does their research in, and that these two things align. Explain in your first email why you want to work with that specific person, what your background is, maybe also include your university transcripts. You do not need to know the professor personally before contacting them.
You should email them and arrange to have a call. Many times, they’ll agree but a big thing is to make sure your research interests align with their work. Why them specifically? Heres a couple pointers: (1) you clearly convey drive and conviction, (2) clearly can explain his/her field and the lab’s general expertise, (3) what are you interested in advancing thats important? (But say you’re open to exploring new ideas too!)
Remember that they must also support a PhD student’s stipend, so it really depends on their funding and pending grants, so ask whether could support you or not - after the main talk.
Recruiting PhD students is part of their job, so you are not spamming them by expressing interest in receiving supervision. But make sure that you keep it concise and that you know their area of expertise.
A short discussion of how to choose a PhD advisor is given in the book "A PhD is not enough" by Peter Feibelman (chapter 3). See this link for an online PDF. Before sending any messages out I would recommend you make a list of advisors that you really want to work with (and knowing yourself the reasons why), rather than spamming a whole bunch of professors in the hopes that one will finally accept you.