If you wanted to be nice, you could try to find out who the previous tenant was.
Perhaps some of your neighbours know him/her, and would be prepared to call him/her up and explain that some mail is still landing in your letterbox.
Perhaps you could google him/her and write or phone directly.
First stop for that would be www.directories.ch
, if he/she is still in Switzerland and is in that phonebook.
You might write a letter along these lines to your landlord:
We moved in to ADDRESS on DATE. Since then, we occasionally receive mail addressed to NAME(s) ON ENVELOPES and, since some of it looks important, we'd like to be sure he/she will receive it.
We realise that, due to data protection, you cannot give us his/her present contact details, but would you please forward the following message to him/her? Thank you.
Since we've moved in to ADDRESS, we occasionally receive mail addressed to you, some of which looks important.
Would you please make arrangements with the Post Office to have your mail automatically redirected? Thank you. https://www.post.ch/post-startseite/...ndeauftrag.pdf
Please contact me on MAILADDRESS (not phone number, so you get it in writing) to arrange a time for you to collect the mail we are now holding for you, until your automatic redirections order is in effect.
Thank you very much."
If you're really nice, and he/she does contact you but for some reason cannot collect from you, you might be prepared to bundle it all up an post it to him/her.