Hi, I'm a designer and a researcher, and I consult with startups on a regular basis.
If your "team is all done to kick off," then I assume there's a stack of documentation that defines who your customer is, the market size, the segmentation, their problems, their mental models, competitive solutions, the things they look for in solutions, etc. That's market research; it's not your assumptions. I also assume there's a database of potential customer contacts, ready to be called in for focus groups, to shadow, to do interviews with, and to test designs. That's customer development.
If there aren't those things, you're not "all done to kick off" yet.
Also,
> How do you make sure that the user experience is what it needs to be?
is a different question than
> How do you start the process that you come up with such interesting interfaces.
I'll answer them in that order.
For any product, you make sure the user experience is what it needs to be by making it for the user. That's it. Yes, coming up with a solution can be a creative act (although it doesn't have to be), but if you can't prove it solves your users' problems, you made art, not a design.
So you "get out of the building." Go find your potential users and understand the problems they have, and the processes they currently experience those problems within. Understand where your potential solution fits into that existing process and their existing mindset and their existing worldview. Make sure they're willing to pay for a solution to that problem in that context.
Then, listen to them. Design your thing, and bring it back to them to test it, using paper prototypes or an interactive simulation or whatever. Watch how they use and react to it. You're not testing the users; you're testing your assumptions and your arrogance. Fix the problems, and then test it again. Every time you think you've "got it," test it again. You only have a solution when it performs the way you (originally, sixteen iterations ago) expect it to with the users. You never make a change and then assume you've sorted it.
By the time you've done all that, you don't have an "interesting" interface any more. You have a usable one. It probably looks pretty boring. It probably works using standard OS controls, or perhaps similarly to their current system but with some efficiency improvements.
That's because your goal isn't "interesting." You're not making a design to impress other designers, or to create something novel, or to challenge your developers. You're making a design to solve a problem for a person that isn't you.
This is why my "design" process starts with creating as little as new as possible. I do a bunch of background research to see what other solutions have preceded me. I look to other industries and other, unrelated products to see what other solutions have similar workflows or inputs or outputs. I know that without testing, any potential solution is as good as any other potential solution. Let's find out how these other solutions perform first. If nothing does the way we want it to, okay, now I'll start coming up with something original and testing that. But maybe some existing thing is perfectly adequate. Great. Look at all the time and money and creative effort we saved. I don't feel like I was cheated out of doing great work because this isn't art. I'm not painting a masterpiece. I'm solving a problem for someone else, and it got solved.
> I'm sure asking this here on HN will help me learn/move fast.
Market research and customer development can be two of the slowest processes in business. That's why most people on HN skip them and go right to code, but then wonder why their product turns out to be terrible. Finding and then recruiting potential customers for your first focus group can take weeks or months. But, you can't build the right thing for your customers if you don't know who they are or why you're building it for them. In this, there are no silver bullets, only lead bullets. There's nothing to do but all of the work.