In Shmiras Shabbas K'hilchasa (chapter 42, 58) it states:
"יכול אדם להתחיל בקריאה זו
של שנים מקרא ואחד תרגום מיד אחרי תפילת מנחה בשבת אחרי שקראו בציבור את הפרשה הרשונה של השבוע הבא״
Now it would seem that one can only start doing Shanyim Mikra V'echad Targum after having davened mincha with a congregation, as is seen from the italicized text. However the author there comments (note 218):
"ומסתבר דהיינו מזמן מנחה גדולה שראוי כבר לקרוא את הפרשה החדשה״
This seems to be explaining the bolded text to mean that one can start Shnayim Mikra immediately after zman mincha gedolah which is the earliest time for the congregation to daven mincha.
I asked one of my Rabanim who has been and is currently a very close talmid of Rav Avigdor Neventzal Shlit"a (who was the longest-lasting chavrusa partner of Rav Shlomo Zalman zt"l) about this quandary and he himself asked Rav Neventzal about it. Rav Neventzal answered that one does not need to actually have davened mincha(neither by himself nor b'tzibur)rather one just needs to start after zman mincha gedolah. I would venture to say that this is the seeming understanding of the author's note.
I could be mistaken about the understanding of the text in SS"K but I know that Rav Neventzal holds this way.