There was definitely a transitional phase in areas that developed agriculture independently. For example, in the mid-east they started out grinding useful grasses. Mortar and pestle and sickle finds start to get more and more common for quite a while before the first full-blown river-valley societies are formed.
Likely they started "weeding" around the better strains, and slowly transitioned to expending more and more effort encouraging their growth (and getting higher and higher yields). A term I've seen in several places for this phase is incipient agriculture.
The anthropologists have their own term for this: Mesolithic. This is essentially defined as the period between Paleolithic (hunting and gathering) and Neolithic (farming).
Poking around, I also see there's the term "Protoneolithic". That could be exactly what you want, but I've never seen that word before just now on Wikipedia.
If you're not into talking about rocks, there's also the term "Horticulture":
Horticulture primarily differs from agriculture in two ways. First, it
generally encompasses a smaller scale of cultivation, using small
plots of mixed crops rather than large fields of single crops.
Secondly, horticultural cultivations generally include a wide variety
of crops, even including fruit trees with ground crops. Agricultural
cultivations however as a rule focus on one primary crop.
I'm less fond of this distinction, as it seems to be used as a way to selectively dismiss the efforts of certain societies, who it could be argued were merely practicing sensible agricultural diversity and crop rotation practices*.
Of course a lot (most?) of the world did not independently develop agriculture, but rather acquired their techniques from nearby practitioners, along with their cereal crops and domesticated animals. These people generally didn't go through much of a noticeable transition period.
* - Native American societies in particular had to cultivate multiple crops, because their main cereal crop lacks an essential amino acid.