Why are the matriarchs not mentioned in the first blessing of the Silent Amidah prayer? What’s the reason the Rabbis who wrote the prayer did not refer to them (directly) in the first blessing along with the patriarchs?

Great question!

It would seem to me, the basic answer here would be that Avraham, Yitzchak and Yaakov are mentioned in this first paragraph because they are the ones specifically with whom G-d made the covenant (Bris Avos) that we are invoking in this blessing. This is clear simply from reading the verses in the Torah. G-d spoke to our Matriarchs as well (they were prophetesses – indeed, the Torah tells us that Sarah possessed a more elevated level of prophesy than Avraham), but G-d spoke to them about different matters. G-d created humanity in two genders for a reason. Each possesses unique spiritual (and physical) gifts. Of course, every human being is different, but these are the general truths.

By the way, I should add that my wife is the one who suggested this answer to me.

Take care,

Shlomo Shulman
JAAM CT
Maimonides at Yale