How to amplify a signal to trigger a function generator?
Going purely by the (somewhat unlikely) results of connecting the trigger input, as reported in the question:

The problem is not a low output signal from the gate itself, but a lack of external pull-up resistor at the output. Note that the datasheet indicates an output current sink rating of 16 mA, but source rating of only -0.4 to -0.8 mA.

Add a pull-up resistor of around 1 kOhms from the output of the gate to Vcc, and the output should trigger the signal generator fine.