First of all: did you do that outside session with the 20# weight vest as a run? If so, that’ll definitely beat you up. Running with a pack is tricky stuff and requires a careful build-up of strength and a lot of attention paid to good technique, otherwise you’ll get at least sore and worse, could develop some acute injuries.
Alternatively, even if you were just hiking it could be that wearing the weight for the first time put such a load on those unsuspecting muscles, hence the soreness. In that case it wouldn’t be anything to worry about, you just want to let the soreness dissipate before doing it again.
Most important to realize is that you have to listen to your body regarding recovery: if you’re very sore after a session, or you are feeling significant fatigue, you have to rest. These signals are your body’s way of telling you that it has gotten its fill of that particular load and needs time to recover – this is how you get stronger. While the old adage “when you rest, you rot” is true to the extent that without regular stimuli a system will diminish in capacity, but those diminishments are minimal when you rest for a day or two, and shouldn’t deter you from making that choice to recover.
Definitely wait until you’re not sore, and you have all your energy back, to do an AnT test – think of it like a race that you want to be fresh for.
With regard to evaluating your progress, you’ll start to see your ability to go a bit faster at the same HR (especially on a treadmill which is so easily quantifiable). You’ll also find that you are recovering faster, and able to train higher and higher volumes each week. You’re right that it doesn’t happen overnight, but as we like to say, when you are starting with minimal aerobic capacity, you have a lot of “low-hanging fruit” to grab and benefit from!