That depends: In a certain way, we are already 4D creatures, with three spatial and one time dimension. However, in these contexts it‘s often useful to only refer to spatial dimensions. The 4D creature then has 4 spatial dimensions, and shares our time dimension.

But maybe its four spatial dimensions are our three spatial dimensions plus our time, and its time is something else completely? Then, by rotating you, it could place your head at a different time than your feet. But that also breaks causality and stuff.

No, Time is 1 dimension for us. It's 1 temporal dimension, not the same as a spacial dimension. When you see someone say 3+1D or 3D+1D, that usually refers to 3 spacial dimensions, 1 temporal dimension.

No, time is not the same kind of dimension as space.

I think the thing here that confuses a lot of people is that we need to use movement over time to help our brains get some sort of grasp on how 4 spatial dimensions could work.

Think of it like how document scanners work: the scanner can only see a thin line, so to read the whole document it has to pass that line over the paper, which takes time.
On the other hand you have our eyes which can see a 2d plane, so we can see the entire paper at once, no time needed.

So the time needed to scan the paper isn't part of the paper's 2-dimensionality, but it's needed to represent it in 1 dimension.

In the same way we couldn't directly perceive things in 4d, but we could rotate a 4d item through our 3d slice until we've seen all angles of it, and then try to build a mental approximation of how it actually looks.

A concrete example: to map a 3d sphere into 2d, you'd move it through the 2d plane which results in it looking like a circle that appears out of nowhere, grows until it reaches the widest part, then shrinks again until it dissapears.
Similarily, a 4d hypersphere passing through our 3d space would look like a sphere that appears out of nowhere, grows and shrinks, and then disappears again.

There are theories that suggest up to 11 spatial dimensions exist like some string theories.