Bezier Warp, Mesh Warp and other distortion effects, including the Puppet tool. Its going to be a lot of work one way or the other and will involve many such effects. No magic solutions.
When you say you want to "3d animate" could you be more specific with what you mean?
I know it is a 2D image, but I want to make it look natural and have a 3D look
thank you !
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You could try recreating it by coping the strokes from Illustrator, pasting them into AE, and using a third party tool like Trapcode 3d Stroke. You could bend the lines a bit and perhaps make it more 3d.
Alternatively, you could bring those splines into Cinema 4d and use a sweep object to make them true 3d lines and then animate that in C4D using deformers.