The question is additional to the question of eating before praying in the morning.
Where is the source for not eating before hearing the shofar?
Is there a permission to eat something in order to help my digestive system start in the morning?
The Piskei Tshuvos brings many shittos. I will bring just a few; see inside for all.
It is completely forbidden to establish a meal before shofar (Tosefta Shabbas cited by Magen Avraham 692:7, and Mishma Brurah 16, Mateh Efraim 588:2, see whole footnote: he compares it to the mitzvah of Krias shma). A 'meal' means more than a kbeitzah of bread or mezonos.
To eat less than this amount is permissible for the sick and people who are weak (Mateh Efraim 588:2) and kiddush is said in private with the eating.
To drink tea or coffee and other drinks which are non-intoxicating, the minhag (custom) is to be lenient (and whether kiddush is needed is a machlokes).
Others are machmir (strict) and don't drink even before prayer, based off the Rokeach siman 353 that the original chassidim fasted prior to the performance of mitzvos like lulav.
Women who are weak, are pregnant, or just gave birth, since they are not obligated in shofar, there is more room for leniency (Chayei Adam 141:7).
Rav Henkin was very strict about people eating before shofar.
This is not for psak: see inside for many shittos (views) on this subject.