This is the 16427th most frequent Polish word.
wczesnego
"Early" (genitive or accusative form).
In this sentence, 'wczesnego' (meaning 'early') is used as an adjective in the genitive singular masculine form to describe 'ranka' (morning), which is also in the genitive singular form.
Na początku wczesnego ranka wszystko było spokojne.
At the beginning of the early morning, everything was calm.
Here, 'wczesnego' serves as an adjective in its genitive singular masculine/neuter form ( depending on the Polish context rules) to describe 'etapu' (stage), in the genitive singular.
Podczas wczesnego etapu projektu skupiliśmy się na badaniach.
During the early stage of the project, we focused on research.
In this instance, 'wczesnego' is an adjective describing 'deszczu' (rain), agreeing in genitive singular masculine form.