The scientific study of the origin of life is called abiogenesis. Basically, the idea is that (somehow) basic self-replicating molecules came about, and over time they became more complicated and clustered together to form cells, which evolved over time to give a diverse range of organisms.
Which of these molecule clusters was the first living organism is not a too-meaningful question; it depends on what we consider life to be (we also face this boundary problem in extant life, e.g., are viruses alive?). Thus, it's only scientifically correct to say that life started from single-cell organisms if we define the boundary to be single-cell organisms, which is a somewhat arbitrary decision.
Now, as for Islam...
If we interpret evolution as compatible with Islam, then we'd go with the scientific reason above, i.e., it depends on how we define "life".
If we believe that life was created around the time of Prophet Adam (a multicellular organism), then no, Prophet Adam would have not evolved from single-cell organisms (by definition).
See: Is evolution compatible with Islam?
In relation to Qur'an 21:30 "... We ... made from water every living thing ...", the essentialness of water for life is established in biology: All known forms of life depend on water (Water, Wikipedia). So this includes single-celled organisms, and it's currently not scientifically controversial (although, if non-water-based life were to be found one day...).
This seems analogous to saying "we make a cake out of flour", where we interpret flour to be a primary ingredient.
For Prophet Adam, we also have: "... He created Him from dust ..." (Qur'an 3:59). Prophet Adam was human (not just a pile of dust), and would have been composed largely of water like all humans.