If you’re a CIO who came from outside IT (or didn’t have a traditional IT background), how did you demonstrate your credibility early on?

I have been leading IT for the last 8 years. My background is in the Supply Chain, Operations and Finance roles during my almost 30-year career. 

1) As I starting my role in IT my first approach was letting the team know that I did not know anything about IT and that they were the experts in their subject matters, and that I was there to facilitate and compliment their jobs by translating the business needs into IT requirements. This empowered the team to make decisions and execute actions with more confidence.
2) I asked top management to become Gartner members so that I could have a technical hand and validate all my decisions. Also, as a way to learn about the IT world. It was an intense learning curve for me.
3) As I learned I could contribute more with the team by giving strategic direction things started flowing more smoothly.
4) I could also communicate the C-Level team what the IT strategy and vision was so I made sure we were aligned to the business strategy.

This is my second time I lead the IT Team and I believe the team has a lot more confidence in working with me as I support them to maximize their value.

I agree with the comments that say to focus on what you bring and be humble and transparent about what you don't know.  I used Gartner's CIO score with my team to understand current maturity of the various IT functions. I also started reporting out on that maturity to my executive team so that they can see current state and trajectory over time. 

1.  First, focus on what you bring to the table.  If you came up a "traditional IT" path (I'm not really sure that exists, but that's a topic for a different post), you'd still have knowledge gaps.  Maybe your "traditional IT" path was in infrastructure, and cloud services and SaaS are weak spots.  Or perhaps your "traiditional IT" path was in ERP, and so you have gaps in networking and security.  Don't be intimidated by what you don't know, because nobody knows everything.  If you're not from an IT background, you probably have a better intimacy with business processes and operations than someone who has spent the last 30 years in data centers:  leverage that intimacy and your leadership skills to deliver.  

2.  Second, learn what you don't know, and do so in a structured way.  Go back to school.  I came into IT mid-career and went back to get a graduate degree in software engineering part-time.   I pursued certifications and continue to take a grad course every year while also reading voraciously.   I think it was Socrates who said that the self-taught man has a fool for his teacher.  Make it a point to learn in a structured way, and hold yourself accountable for that.

3.  Third, focus on trust.   We had a saying in the Army that was particularly important for those of us fresh from college:  "Your soldiers need to know that you care more than they care about what you know."   You're in a technical leadership slot, but the "leadership"  and not the "technical" is the key word in that clause.  Build trust with your team and within your team, and with the business partners that you and your team serve.

I actually had a CIO come in who was not technical, and I was impressed with his approach.  As the most senior "technical" person on the team, he approached me and offered to "partner" with me.  "You show me what you know, I'll teach you what I know".  We started with an extremely deep dive exercise where we broke down the entire IT department into discrete functions and responsibilities and then we built a generic Org-chart with the specific responsibilities assigned.  We then compared that to the existing organization to ensure that folks were in the right roles.  Lesson 1 in CIO Leadership was complete.