随着(suí zhe) - along with, as, following in Mandarin

随着 (suí zhe) marks one thing changing in step with another. English usually reaches for "as" here, and that is the safest gloss: 随着时间过去 is "as time passed", not "following time passing".

It is a preposition, so it takes a noun phrase or a nominalised clause and sits at the front of the sentence. The main clause that follows almost always describes a change rather than a state, which is why 变 (biàn, to change), 越来越 (yuè lái yuè, more and more) and 起来 (qǐ lái, marking the start of something) turn up beside it so often.

The trap is confusing it with 跟着 (gēn zhe), which is physical following: 跟着我 means walk behind me. 随着 is abstract accompaniment. Swap them and you get either a person trailing a decade around or an abstract idea walking down the corridor after you.