1. For any non-temporal causal regress, that regress is either finite or infinite. (Definition)
2. The causal regress of X is an attribute of X. (Premise)
3. If every observable attribute of X is finite, then the causal regress of X is most likely finite. (Premise)
4. Every observable attribute of X is finite. (Premise)
5. Therefore, the causal regress of X is most likely finite. (From 1 – 4)
Take, for example, my favorite illustration of a watch. The causal regress of one gear turning to cause another gear's turning is an attribute of the watch - in support of our second premise. (3) introduces induction to the argument. If attributes A, B, C, and D of X are all observed to be finite, the likelihood that E of X is also finite is increased significantly. Moreover, if all of the known attributes of X are finite, and none of them are infinite, it follows that all of X's attributes - both known and unknown - are most likely finite.
For any non-temporal causal regress, then, it follows that the regress itself is most likely finite, given the finitude of every other attribute. In arguing for a metaphysically necessary non-temporal First Cause, the inductive argument against an infinite regress may be combined with the following argument:
1*. Every existing entity is either contingent or necessary. (Premise)
In this context, an entity is contingent if it has its existence in another; and it is necessary if it is self-existent, and exists simply by virtue of the fact that it cannot not-be.
2*. If a non-temporal regress of causes is finite, then a metaphysically necessary First Cause exists. (Premise)
3*. The non-temporal regress of causes is most likely finite. (Premise)
4*. Therefore, a metaphysically necessary First Cause most likely exists. (From 2 and 3)
I tend to think that this argument is also applicable to strictly temporal causal events. So long as time is an attribute of a thing, the inductive argument may be modified to fit this change of focus.