By competition and diploma.

What sort of competition and diploma?

Who do you compete with over what/in what way and who controls the competition/decides the winner? Is anything that influences this process political?

Does requiring that judges be elected remove requirements for diplomas? It definitely increases competition as you have to compete for the will of the people.

Why elect him on political bases?

Everything is political. The laws are determined by politics, every single person's interpretation of said laws is determined by politics.

A better question is, how does your system actually effectively remove politics from the process? Or does it simply shift the political aspect from the people themselves to another third party?

Why shouldn't the people themselves decide how they want the laws enforced in their own country? Who else should decide if not the people?

We do not elect an engineer on political criteria, we take the one who seems the best among the candidates.

Who determines which engineer seems the best off of what criteria? Is it political at all?

Example: engineer1 is great at building bridges but only alright at apartments, engineer2 is great at building apartments but bad at bridges.

The people of the city know the city requires more apartments but not more bridges.

Why should engineer1 get the job for simply being the "better engineer" when he doesn't fit the needs of the people?

What's the point to elect them?

Why shouldn't a judge serve and be accountable to the will of the people? Who knows better? Why?

And how is it not an authoritarian, anti-democratic, political opinion to state that someone does better know what the people need than the people?