I'm new to the game, and just got enough resources to craft my first golem, but it's asking me to chose a pet, and I just want to know if that pet disappears, or like, what happens?

Your pet doesn't disappear. It spends four hours crafting the golem. Once the golem is made, your pet comes back with zero energy.

Your golem "lives" to produce a certain amount of material per day for ten days. After the tenth day, the golem collapses and you have to puild the golem again.

All golems live for ten days, then collapse.