One of the reasons I like the First Cause argument is that there are fewer problems with it than without it. E.g. Assume something that changes is the origin of time and change and you have a self-contradictory statement.
But to your question, one answer to how something that is unchanging can create change and time is "by just existing".. "by it's existence."
And, "suddenly" is another word that depends on time - so it doesn't apply. After time exists, then you can have "sudden," until then, no.
Is God eternally creating or did he, in his eternity, not always create? If you believe the latter, which is the First Cause argument, then the we have the paradox that an unchanging God would have had to change in order to begin creating!
On the other hand, if the ever-changing universe existed forever, then nothing had to change for the universe to exist and repeat itself eternally.