I've noticed the bugs have begun to sing at night lately.
「夜に虫の音が聞こえ始めました」は
ーI've started to hear the sounds of bugs at night.
「夜に虫の音が聞こえ始める」
ーI've noticed the bugs have begun to sing at night lately.
「最近夜に虫が鳴き始めたのに気がついた」
のように言えます。
例:
It's still hot these days, but I've started to hear the sounds of bugs at night. It feels like fall is on its way.
「まだ暑い日が続くけど、夜に虫の音が聞こえ始めました。秋の気配を感じますね。」
ご参考まで!