Is it possible to make no mistakes all the time?

There are established methods to eliminate mistakes, usually this takes the form of redundancy. The airline industry is built on this principle, where every action is checked several times by different people. But despite this safeguard, I would say no, it is not possible to never make mistakes.

No, because we are human, we error.

But in life, I can't tell most people that I am only a human and I error, especially at work.

How much do you make mistakes at work? What kind of mistakes/

Perhaps this is not the right place for you.
Your job should be gratifying and help you grow as a person. If it does not, change jobs.

Yes, it is possible, but very, very difficult.

For example, i once made a mistake. I thought i was wrong, but upon investigation, discovered that i was actually right.

Only if you are the ruler of North Korea. He just has you jailed or killed if you tell him he is wrong.

Otherwise, it's one of the best ways to learn. The bigger the mistake the less likely you will do it again. No one can become an expert without first experiencing all the things that can go wrong. Perfection can be very boring.