The PCB tested was built with 4.7uF 25V X7R and 0.1uF 25V X7R caps decoupling the DC power supply for the 555 and the 74LVC1G04 inverter. The circuit is simple enough that it was built on a 2 layer board with almost all of the back side of the board as a ground plane, and about half of the front side of the board as a power plane.
All of the tests shown were run with 5.0V into the board from a bench supply. The PulseGen board was connected to an SMA to BNC adapter and a BNC gender bender to connect into the scope input as closely as I could. The scope was set to 1:1 input with 50Ohm termination.
Here is a scope shot of the Rise Time of the pulse captured at 1nS/Div
Some overshoot/ripple can be seen at the rising edge, rather more than I was hoping for.
Next, the same configuration captured at .5nS/Div
The rise time looks like about 0.75nS. I was curious if the slight excursion below ground at the beginning or the overshoot at the end of the rise would be visible on the power supply for the '04, but it was not. The power supply looked clean when viewed on another scope channel.
Here is a shot of the fall time at 1nS/Div
It looks to be a similar period (around 0.75nS), with some ringing at either end. Here it is captured at 0.5nS/Div
So the long answer is yes, you can generate sub nS edge rates with a 74LVC part. Honestly, I was expecting edge rates about 10X these, so I learned something.
5/21/2020 Update: After seeing a comment in a test equipment mailing list that the output impedance of a 74LVC device is about 7 Ohms, I changed the series resistor on the output from 51.1 Ohms to 43.2 Ohms. This reduced the overshoot on the rising edges and undershoot on the fallin edges, as can be seen in the screenshots below.
Comparing the original screenshots using the 51.1 Ohm series termination resistor to the ones using the 43.2 Ohm resistor, the ripple prior to the beginning of the transition is lower with the 43.2 Ohm resistor as well. Negative time delay?