I was wondering if it’s possible to extrude a sphere out of a flat surface (that makes the bottom of a cylinder)? If it is, how do I go about doing that?

If it isn’t, is there an easier way for me to shape a cylinder into a sphere other than moving the vertices one by one and hoping for a decent result?

It is. Wouldn’t normally do it like that but connect a sphere that was added to the cylinder, but it’s possible. For one it needs enough geometry, then could use to sphere function with an appropriate pivot, shrinkwrap or cast modifier with a vertex group and a helper object.

That’s all Greek to me. Though it seems like you’re telling me to create another mesh, a sphere and then connect it to the cylinder, instead of extruding? Because extruding the sphere from another form would prove more difficult?

I’m a bit new to 3D modelling, so my apologies if that’s normally an easy thing to do.

Furthermore, you speak of geometry; what did you mean there when you said that? What did you consider ‘‘enough geometry’’? Did you mean the faces?

of those, middle edge loop selected, scaling along Z with proportional editing in connected mode enabled which concentrates more cuts in the middle

filling the top with grid fill

all faces from the top selected minus one edge loop, to sphere tool with the influence of 1

scale up

and the resulting lollipop that didn’t need to be modeled like this

More faces/polygons than what a flat surface on a cylinder typically gives. There are three face types, any will do as long as there are enough of them to form a sphere, and enough is the amount that is needed for you to call it a sphere.

Cylinder primitive cap options: none, n-gon, triangle fan. None of those are suitable for a sphere, which is a curved form and needs a lot more polygons than a flat one.