There is an ongoing equilibrium reaction that binds and dissolves phosphate to/from calcium carbonate (your rockscape and substrate). If your rocks are not sufficiently saturated, more phosphate will be bound than dissolved, so your tests will show 0ppm, especially if they aren't very precise. Once the rocks are sufficiently saturated, phosphate can rise. For the same reason, water changes tend to be quite inefficient when trying to reduce phosphate levels, because buffered phosphate will just redissolve.
To save a few bucks, I recommend using a DIY recipe to dose phosphate and slowly saturate the calcium carbonate:
https://www.reef2reef.com/threads/diy-phosphate-dosing-recipe.1109919/
This can take quite a while. I remember dumping insane amounts of phosphate into my tank until phosphate started to become detectable.
If nitrate is also an issue, I recommend dosing ammonia in frequent but small batches instead of supplying nitrate directly:
https://www.reef2reef.com/threads/diy-ammonia-dosing-for-low-nitrate-systems.987087/
Ammonia is the preferred nitrogen source for corals, algae, and bacteria, as nitrate has to be converted back to ammonia first before these organisms can get to the precious nitrogen they actually want (there may be a few exceptions to this rule). This conversion requires energy and precious trace elements that can limit the actual nitrogen uptake.
Of course, you will also have a lot of biomass forming as dinoflagellates, biofilms, and algae grow, so a lot of those nutrients will be bound to biomass and therefore no longer detectable by your tests. Once all surface area is overgrown and the population of all sorts of organisms has reached a peak, you may be able to see nutrients increase as other elements/molecules become the limiting factor. Carbon, for example, can be a limiting factor, so people use "carbon dosing" (adding alcohol or acetic acid) to encourage bacteria growth. Iron is also a very common limiting factor because it is needed for many processes in a reef tank, but the actual concentrations of it are very low in natural sea water.
When starting a tank with dry rock (my current system, running for 6+ years now, was started with 100% dry rock and substrate), it is fairly common to have very low nutrients
for a long time. That's why I'm dosing ammonia and phosphate
multiple times daily to maintain stable nutrient levels. It's a bit difficult at first, but after a while you get to know your tank and see how nutrients will react in relation to each other. It makes it easy to maintain nutrient levels within your preferred target ranges once you get the hang of it, and I prefer it over having to constantly try to keep them down.
If Dinoflagellates are a symptom or the cause of low nutrient levels is a bit controversial, so some people recommend dosing nutrients to get rid of them while others say dosing nutrients will just feed them. I think both things can be true, so you should just try it out :)
