Here are some examples of GINOMAI (the aorist middle form EGENETO is employed in John 1:14) and brief comments about how it is utilized in each cited verse:
Matt. 4:3-used by Satan who asks Jesus to make some stones become loaves of bread.
John 1:3-John writes that all things (PANTA) came into being through the LOGOS.
John 1:12-Humans who exercise faith in Jesus and receive him are given the authority "to become" (GENESQAI) God's children (TEKNA QEOU).
John 1:14-The LOGOS became flesh.
Heb. 11:3-TOUS AIWNAS came to be out of things that do not appear.
Cf. Matt. 5:45 and countless other examples.