1. Possibly, a First Cause in the order of sustaining causes exists. (Premise)
2. Necessarily, whatever exists is either contingent or necessary. (Definition)
3. Possibly, whatever is contingent has a sustaining cause. (Premise)
4. Hence, a First Cause cannot exist contingently. (From 1 - 3)
5. Therefore, a First Cause exists necessarily. (From 2 and 4)
The logic here is airtight. So long as it's even possible for a First Cause to exist, and it's even possible that whatever is contingent has a sustaining cause of its existence, it follows logically and inescapably that a First Cause (in the order of sustaining causes) exists.
Of course, what remains to be seen is whether this First Cause possesses any or all of the divine attributes.