It is possible to build stairs at almost any angle, but if they are too shallow, they can feel strange to walk on, and it might be better to create a landing and then continue with stairs. There is also a limit in steepness when the step height is more than 20-22 cm, as it becomes uncomfortable to walk down, and it is then technically called a ladder.
For a staircase to be comfortable, there are various rules of thumb. A common one is that 2 times the step height + 1 step length should be between 560-650 mm.
In your case, if you make the stringers of 45x220, it will suffice to have footings at the ends.
My recommendation is also to make the treads out of 45mm thick material, as thinner can become springy after a while.