From a purely politically correct standpoint, there are many mushy answers you could give. Any spin on what the people above me wrote would work.
In truth, though, you’ve asked a stumper. Why would a completely irreligious Jew be proud to be Jewish?
We say every night in Krias Shema Al Hamitah, “Ve’Atah Hashem magen ba’adi, kevodi u’merim roshi…” Hashem is my source of pride. That’s the source of Jewish pride.
Without God, what is a Jew?
That being said, an American takes pride in his/her country’s accomplishments. A black person will take pride in black people’s accomplishments.
So you could point out to this group in plain statistical terms the huge percentage of “accomplishments” which Jews have garnered. Think Hollywood, Nobel prize winners, leading medical researchers, and even the military power of the IDF.
Though this is not the true Jewish pride we as religious Jews strive for, it can definitely instill a feeling in them that God is clearly on our side.