According to this Star-K article
On Shabbos morning, men may drink water, tea or coffee before Shachris
(after brochos), but may not eat and may not drink “chashuva
beverages” (e.g. alcoholic beverages) unless they are required for
health purposes. After Shachris, one may not eat or drink until after
A woman who normally davens may eat or drink before davening after
reciting morning brochos. According to some Poskim,42 on Shabbos if
she needs to eat before davening, she is not required to recite
Kiddush at that time. Once she has completed davening Shachris, she
must hear Kiddush before eating or drinking.
My understanding of the above is that you can have coffee as long as you haven't started Shacharit, and you would have to say the "birkot hashachar" first, anyway. Once you have past that point, you have to wait for Kiddush, if you're male.
FWIW, this would explain the "schnapps clubs" in many shuls, where people make Kiddush between Shacharit and Musaph. (Many shuls in my neighborhood, have a no alcohol policy which includes no wine, as well. Kiddush in shul is said on grape juice.)