Can we make a machine that create same amount of positive and negative energy?

Then I search for energy of the universe. I was surprised that total energy of the universe is zero.

I would like to emphasize the inherent ambiguity of the term “energy of the universe”. So, when people say that total energy of the universe is zero they either mean something highly technical and in a certain sense trivial (e.g. Wheeler–DeWitt equation) or making a lot of unwarranted assumptions about cosmology. See also this discussion.

Then I was thinking that is it possible to make a machine that creates both positive and negative energy of the same amount at the same time.

You undoubtedly have already encountered negative gravitational energy that is supposed to balance the positive matter energy on cosmological scales in a well known equation of Newtonian gravitation theory: $$ U = -frac{G M m }{r}.$$ Note the minus sign! General relativity in a sense is just an extension of Newtonian gravity even when applied to cosmology. So negative gravitational energy is created whenever a mass is lowered in a gravitational field and by energy conservation the same amount of positive energy in various forms is created simultaneously. Hydroelectric power plant is thus an example of machine that produces electricity (and various forms of waste energy) and creates negative gravitational energy at the same time.

Of course, lowering masses might not seem too exciting, but keep in mind that gravitation powers the most energetic processes in the Universe such as quasars.