Richard Swinburne has been known for his many inductive arguments for God's existence, one of them being strictly cosmological. This is my own take on an inductive cosmological argument, which is by no means comprehensive.
1. The uniformity of nature is either caused or uncaused.
2. Complex things are unlikely to be uncaused.
3. The uniformity of nature entails very complex things.
4. Therefore, the uniformity of nature is probably caused.
(1) shouldn't be controversial. Something "uncaused" could logically be either self-sufficient or even a brute fact (although I don't personally believe in brute facts).
(2) can be supported by an analysis of things we know that are complex. Always, or for the most part, whenever we observe a complex entity, we discover that it is caused by the formation and unification of its diverse parts.
(3) simply points out that nature contains many complex elements, and I don't think anyone will disagree with that. As a result, I think (4) is more likely true than its negation, which would make this a cogent inductive argument.