There's already quite a few of builds of cheap pulse/step generators online, so I just picked one to base my build on:

Even though something like a 555 timer could generate the start pulse to feed the Schmitt trigger, I ended up putting a XIAO RP2040 to just generate a pulse via PWM. 

I put two edge launch SMA connectors so I could run one to whatever I was trying to test and one to my oscilloscope.  The theory behind simple TDR measurements assumes that there's only one transmission line involved and adding the second one to the scope would cause it's own set of reflections into the high impedance scope termination.  So I added a 50ohm termination at the scope, which I have to do with an external passthrough termination:

The 50 ohm termination will load the signal, which will cause the magnitude of the signal to be decreased compared to when the scope isn't connected, but that doesn't matter in this case since it will only be used with something attached to make the reading.  

This pulse has a rise time of a little more than 1ns into 50 ohms, which is about the limit of the bandwidth of my 350MHz scope.  

Attaching different lengths of coax shows that the basic TDR measurements work.  

Which results in the following trace:

The orange ref trace is when nothing is connected.  The active trace is with a 2ft coax attached.  The green trace is with a much longer coax cable attached.  The different length of coax cause a step from the delayed reflection off the other end of the cable.  The length of that delay is proportional to the length of the cable.  That same delay is what I'm aiming to measure to in soil.  

Now I need to make something to probe soil and see the TDR measurements.