Asked the inverse of this here but when I thought about it I preferred the opposite sentiment. Not that one exists because they make things but that they make things because they exist, as in there is no other choice. It is a compulsion of existence.
Anyways, would there be a proper translation that would make sense for "I exist, therefore I make"? (So the inverse of "Facio Ergo Sum".)
In general, you can translate "I X, therefore I Y" into Latin as X ergo Y (with appropriate conjugation of the verbs). Even more so if you want a reference to Renatus Cartesius. The only remaining question is to find appropriate translations for the verbs.
As discussed in the previous question, "I am" is well translated by sum and "I make" by facio. Thus sum ergo facio is a good translation in the specific case you ask about.
You can easily construct similar phrases with other verbs. Many dictionaries list verbs with just the right form (present active indicative first person singular), so you only need to find the verbs that fit your needs. If you want to explore different options, I suggest you start by entering an English verb of your choice to some online Latin dictionary and then look at the translations from Latin to English from each candidate on your list of Latin verbs.
Was using this for something else, but I think this may become a tattoo :P – Adam Haile Jan 31 '17 at 00:12