Keeping in mind I thought of this argument around a decade ago, you also might suspect I've cleaned it up a bit. Your suspicion is justified.
1. It is possible that nothing exists. (Assumption)
2. If nothing exists, then possibility does not exist. (Premise)
3. If possibility does not exist, then it is not possible for any state of affairs to obtain. (Premise)
4. (1) is a state of affairs that obtains. (Premise)
5. Therefore, (1) is false. (From 1 - 4)
I went on to argue, much less transparently:
6. The concurrent nonexistence of all contingent things is possible. (Premise)
7. Therefore, something necessary exists. (From 5 and 6)
Of course, the argument was (and is) very underdeveloped. It assumes things like "possibilities exist," which are at least relatively contentious. Also, the necessary entity of (7) prima facie could just be the set of possibilities. As a more informed Thomist than I was then, I now recognize that possibilities or potentialities cannot obtain unless there is something actual. I then fell back on the argument from change.