Are there any English sayings to the effect that little changes may lead to big changes?

Can you think of any sayings about change, especially ones expressing

• how a big change must begin with a little change?
• how certain institutions, ideas, or God remain eternally unchanged?

Note: the above is an edited version of @lovespring's question. See edit history for original question.

Something like these?

• “Mighty oaks from little acorns grow”
• “A journey of a thousand miles begins with a single step”

It's not yet a saying per se, but the so-called butterfly effect is a modern theme popular in certain circles and commonly referred to in modern speech.

So, people sometimes say things like “the flap of a butterfly’s wings in Brazil might set off a tornado in Texas”

The type of saying I think you’re looking for is called a proverb. There are plenty of online resources for those; for example, this list on Wikiquote.

On the subject of change, you might like the saying:

Plus ça change, plus c’est la même chose

Even in English speech or writing the original French is used, or it can be rendered in English as:

The more things change, the more they stay the same

Small streams make large rivers

tongue-in-cheek

A small step for man ...

Here's another answer: The "for the want of nail..." proverb, which is somewhat related to FX_'s answer, the Butterfly Effect, in that both proverbs emphasize the power of insignificant things to cause momentous changes further on. However, in my observation, the Butterfly Effect is mostly referenced neutrally, and a few times even positively, say for example when describing the power of small act of kindness to enable the performer to reap larger "karmic" rewards later. On the other hand, the "for the want of the nail..." story usually has uniformly negative connotations, in emphasizing the role of unpreparedness in causing momentous tragedies in ventures of a complex nature.