Is it wiser to build relationships with potential sponsors early on? Or to allow for the listenership numbers to grow before reaching out?

Without knowing much about your podcast or ultimate business goals here, I would say reaching out to the potential sponsors to at least get a feel would be a good idea. You might even consider some promotional sponsorship rate for one or two sponsors to get in early. If you have a marketing plan to show how you are going to work to drive the traffic necessary to make their sponsorship worthwhile, then they might be willing to take a chance on you early. Rewarding them for taking that risk with a slightly lower rate could be good for both of you. Good luck and enjoy!

I'd imagine that adding sponsors after the fact is hard for your listeners to take vs you just launching and having a established sponsor.

Like most questions, the answer is, it depends. ;)

It depends on what your podcast is, the audience you're trying to reach and, most importantly, the #1 goal for your show.

Podcasting is the wild west. There are no right ways to do it and I'm seeing over and over again that the people who are succeeding are coming up with creative ways to make money.

Sponsorships are only one of many ways to "monetize" a podcast. But it's hard to say which direction is best for you without knowing more about your show, your audience and your goals.

I'm happy to help any way I can, so feel free to reach out anytime.

If you haven't already, reach out now and let them know about your show. Tell them a little bit about the content and how often you plan to release episodes. I'd even try pitching them on a deal and say you're offering a special reduced rate for sponsors who come onboard early. Either way you don't really have anything to lose. Worst case, they'll tell know what kind of numbers they'd like to see for a sponsorship commitment.