I'm going to differ from Ethan Bolker and say you should consider it. It's not a concern that you are invited even though you're not a professor, because there's no rule that says only professors can join editorial boards. There is a requirement that you be an expert on your field, and sufficiently senior postdocs will be an expert on their field (I'd even argue that fresh PhD graduates are experts on their field, it's just that "their field" is very narrow so the scope of papers they can handle is also very narrow). Furthermore, as you write, you have no evidence they are untrustworthy. All new journals start by forming an editorial board, which matches what you're seeing.
That said, you should evaluate the offer similarly to how you evaluate offers to collaborate (which is effectively what this is). Things you should figure out:
- Are they an open access publisher or hybrid (fully subscription publishers are practically non-existent at this point)? If they're publishing subscription content, the chances of them being predatory (in the traditional sense of the word) plummets, arguably to zero. However, the fact that you could read the papers on their website suggests they are open access.
- What do they expect from you? Are you only handling papers, or are they expecting something else (you to submit papers, represent the journal at conferences, attend editorial board meetings, set the journal's strategy and direction, lead some special issue, etc.)?
- How many papers do they expect you to handle? You need to know this to estimate how much time commitment is required. If you've never edited before, it can be hard to tell, but get a concrete articles/month number and you can consult a more senior academic to convert that into a time estimate. For new journals it can be extremely hard to provide this estimate (because new journals struggle to get submissions), but you still need an upper limit beyond which you simply cannot spend more time on the journal.
- How much support do they provide? On one extreme you have publishers which pretty much do everything and expect only a decision from you. On the other extreme you have publishers which expect you to do everything, and they only start getting involved once you decide to accept a paper. Needless to say the latter is much more time-consuming for you, but the peer review process will generally be less controversial because you have direct oversight and you can be expected to do a better job than the publisher.
- What benefits do they provide you? If you're one editorial board member among many, it's highly unlikely they will pay you a substantial honorarium, but they might offer other benefits (e.g. travel grants, waived APCs).
You also want to evaluate:
- Who are you talking to? Most probably it's another editorial board member, or an employee of the publisher. In both cases, you could have a serious conversation with them. You could ask them what kind of niche they see the journal occupying, what competitive advantages the journal will have, how they plan to compete with established journals, etc. These are all difficult questions that tell you how serious the journal/publisher is & how experienced the journal leadership will be.
- In the same vein, if you're talking to an employee of the publisher, you might be able to find out more about them from Google. Another thing would be to see how straight they are with their answers. If they're using vague language & it's unclear if they understand you, then communicating with them in the future could be frustrating.
The point of this is that starting a new high-quality journal is a very difficult thing. If the person you're talking to doesn't realize how much of a challenge it is, then they can't be very experienced with publishing, and there's a high chance the journal will fail. I would be more inclined to decline then. Also, you can email the editor-in-chief even if you don't know them (they will be receiving quite a few emails from people they don't know, asking about the submission process).
Once you have all the information, then you can answer the question: given what they are asking from you and what they offer in return, is it worth taking up the offer? This isn't that dissimilar from an offer to collaborate on some research project - they both take up some of your time and offer something in return. It's up to you to decide if the 'something in return' is worth the time you'll need to invest. If you're still unsure, you could try talking to your postdoc supervisor about it.