ichidan verb
start to come; begin to arrive
Compound of 来る (to come) and 始める (to begin). Used when something or someone starts coming, arriving, or appearing. The gloss 'to become for the first time' is a rare or awkward translation; the core meaning is the beginning of coming/arrival.
春になると、渡り鳥が来始める。
When spring comes, migratory birds start to arrive.
新しいお客さんが来始めた。
New customers have started coming.