How do you find a big problem in the market?

Watch them work. When I'm doing validation, most of my discovery consists of me just watching them work. Shadow them for a day or an hour or whatevwr, watch what they do, ask questions about things that seem crappy.

It's ok to be an aspiring opportunity that's just out to learn more. Anytime I've asked for access like this, I've been granted access. No agenda, no selling, just learning.

Find out what they already pay for. Not what they use for free or what they wish they had. Only what they actually pay for right now. Could they pay you instead?

Big problems are aplenty. Find any niche, ask them for their 3 top problems. I bet you get plenty of responses. People love bitching about their biggest frustrations.

The only problem is that not all big problems can be solved by software. Some might be partly alleviated by software, but a lot of it is not something some lines of code can solve. Your best bet, as @marcusstenbeck mentioned, is to look for big problems they're already solving by paying for software. That way you know it's a big problem, software can solve it, the customer believes software can solve it, and they're willing to pay for it.

The challenge then is to get them to switch to you. So how you position and differentiate will be key. But at least you can skip the "educating the market" part when you try to solve a problem that's unsolved by software thus far.

Look at new technologies coming out and see if they can be applied to older processes.

Focus on the world you’re involved in, directly impacted by, and have access too. That way it’s less education on your part about the basic stuff and necessities. You can then jump right in and get to the root of the problem quicker. It’s hard to solve a problem or disrupt an industry when you’re stuck learning the fundamentals & taking 101 classes. It can be done but this adds more challenges to an already difficult road. Trust me I learned the hard way!

This is a very good question, your users might not know they have a problem yet, empathy and becoming an user yourself should bring more awareness and therefore help you with this. I don't think there's a magic bullet.