I saw a bunch of deer near my house all of the sudden when I went out for a walk.
この場合、次のような言い方ができますよ。
ーI ran into a herd of deer in my neighbourhood.
「近所で鹿の群れに出くわした」
to run into「出くわす」
a herd of deer「鹿の群れ」
ーI saw a bunch of deer near my house all of the sudden when I went out for a walk.
「散歩中家の近くで鹿の群れに出くわした」
to see ... all of the sudden を使っても「出くわす」を表現できます。
a bunch of deer「たくさんの鹿・鹿の群れ」
ご参考まで!