Should I ask for a LOR from my future Master's Supervisor?
I would ask them now if they could imagine writing a letter, either now (outlining the reasons why they took you as a student), or close to Dec 1st.  But I would phrase it in a way where it is clear that you don't expect them to do it, since they don't know you well yet.  This way, your prospective supervisor can choose whatever they prefer - either they are happy to do it, or they will tell you that they can't judge you sufficiently well and that you should ask someone else (this is what I would do).
What I wouldn't do is to wait until close to the deadline and ask them then - first, if they say so you have to find someone else within a very short time (and most people don't like this, understandably), and second, this might come across as some kind of blackmailing (&quot;I need your letter, since now it is to late to get someone else's&quot;).
In any case, good luck with your application.
(P.S.: As always, adding context about the country/region in which you are doing your master and in which you are applying can help you to get more tailored answers.)