Translation:First, you pass by a small bank.
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In the possessive case, AのB typically means "A's B" or "B of A". We also see の used to couple nouns to postpositions, and you're wondering if this is a different usage case. Well, 机の上 (つくえのうえ) means "on top of the desk" (B of A). テレビの前に is "in front of the tv". 銀行の側 (ぎんこうのそば) sort of means "the vicinity of the bank" or "the bank's vicinity" (A's B). I could be wrong, but I believe that the particle follows the same rules here as it does with possession.
So if you want to think of the の particle as serving a possessive function in postpositional phrases, I don't think it could hurt. Just know that in sentences like "the cat is under the table", it's still テーブルの下に猫がいます, even though there's no explicit possessive relationship between "table" and "under" in the English sentence (i.e. "the table's underside").