One of my favourite problem solving sayings comes from a Mathematician by the name of George Polya. He is famous for the 4 step problem approach which you have probably encountered in some modified form in business, software development and problem solving.
Attribution: Pixabay - geralt
The phrase that I really like from him is "If you can't solve a problem, find a problem that you can solve and solve it."
This might sound like lazy talk, trying to ask us to avoid taking on hard problems, but that isn't the point. What it it really is about is working on the hardest problem that you can solve.
There are several ways to go about finding problems you can solve.
Break the large impossible problem into lots of little ones
The most common advice for dealing problems is to turn big problems into little ones. Every supposedly difficult problem is made up of lots of easy ones.
attribution: Flickr - Patrizlo Cuscito
Of course some of these little problems could be very difficult, but when taken as single item it is much easy to deal with.
Do what you can now
I have had many jobs where, when I start, the task before me looks impossible. Instead of trying to work on problems that I can't solve, I grab those problems that I can solve and start on them. Sure I am avoiding a lot of work that needs to be done, but usually by doing other work that also needs to be done.
Attribution: Flickr - Sebastien Wiertz
Once I have solved the easy tasks I start working on the harder ones, then putting in place systems and finally arriving at a point where everything is progressing smoothly.
Find other problems
Polya's main point was always that students would be given mathematical problems that they couldn't solve. So they would become frustrated and give up. His solution was if you can't solve this problem, search around until you find ones that you can solve.
Attribution: Pixabay - Nemo
Work your way up to success by working at your level but also always moving up.
Be always moving up
To re-iterate that points made. It is isn't about ignoring problems or challenges. It is about starting at your own level and moving up to take on harder and harder problems.
Attribution: Flickr - Georgie Pauwels
You don't have to start on the most difficult problems, only the ones that are a challenge for you now, and when they become easy, it is time to move on to the next challenge.