First of all, God does exist outside of time, so there's nothing impossible about that. That's what is often referred to as God existing in eternity. Concerning the creation, Augustine specifically addressed that question:
"Those who say these things do not yet understand thee, O Wisdom of
God, O Light of souls. They do not yet understand how the things are
made that are made by and in thee. They endeavor to comprehend eternal
things, but their heart still flies about in the past and future
motions of created things, and is still unstable. Who shall hold it
and fix it so that it may come to rest for a little; and then, by
degrees, glimpse the glory of that eternity which abides forever; and
then, comparing eternity with the temporal process in which nothing
abides, they may see that they are incommensurable? They would see
that a long time does not become long, except from the many separate
events that occur in its passage, which cannot be simultaneous. In the
Eternal, on the other hand, nothing passes away, but the whole is
simultaneously present." (Confessions, 11.11.13)
The key to understanding what he is saying is to remember that any concept whose meaning depends on a temporal idea needs to be omitted from any questions or descriptions of the eternal. For this reason, even the term creation must be understood in a way that does not imply time or change. From the human perspective, the creation involved a series of events in time, each of which involved change. However, from the divine perspective, the creation must be seen as an eternal expression of God's will. We see it as a change, but there is no reason to assume that He sees it that way.
It's interesting that many mistakenly think of God's existence in eternity as a limitation to what He can do or how He is, but that's really looking at it backwards. Existence in eternity implies a liberty that is not easy for us to comprehend since we are subject to temporal constraints. How could freedom from these constraints ever constitute a limitation?