This still has the premise that "everything that exists needs a cause." If you take this premise, all you have are dependent causes - the infinite regress, and the result that nothing exists because the "cause" buck is passed on infinitely. Turtles all the way down.
The first cause argument does NOT use this premise, therefore it's not violating itself by having something exist that is uncaused. In the First Cause argument everything in motion needs a cause, everything dependent, changing, in time, imperfect needs a cause. This set includes everything we sense in the universe, everything in space time.
The First Cause is not in motion, independent, outside time, perfect and unchanging. Therefore it is not in the set of that which needs a cause.
Looking at it strictly logically:
Assuming everything must have a cause as a premise, results in nothing existing (all dependent causes lacking the necessary independent cause). The first cause argument avoids this obvious failure.
Can anything change anything else, without itself changing its changeless state?
We can just as easily than presume that space/time/energy ("chaos" if you will) is the UNcasued cause that collapses and inflates over and over ad infinitum.
The First Cause is not in motion, independent, outside time, perfect and unchanging.
Then what is "Let there be light!"? That "unchanging" First Cause has just changed!
The first cause it to bring something into existence before it can cause it to move, so that everything that we say "is" or "exists" had to be caused to exist. Therefore the first cause cannot exist, cannot "be".