Deeper theological considerations aside, I think the first program might be
the WHILE loop, as demonstrated in the clepsydra, an ancient water clock.
While the weight of a cup being filled by a regulated flow of water is less
than an opposing weight, the cup fills.  When it exceeds the test, it causes
the balance arm to move, advancing the clock and emptying the cup.

Clocks are wonderful examples of machine logic, and clockwork mechanisms are
great fun to study in terms of programming.