I have a question pertaining Kant's transcendental philosophy.

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I have a question pertaining Kant's transcendental philosophy. This question can be applied to both the pure intuitions of space an time and the categories of pure understanding, but I will articulate my doubt dealing only with the pure intuitions of space and time (for the sake of simplicity).

Now, for Kant, space and time are not properties of the world, according to him, our cognitive apparatus applies the spatial/temporal structure to the world. The reason for this is that we cannot derive space and time from our experience of the world, since we need space and time to even be able experience the world. Space and time are the necessary conditions for sensibility.

So, to say again, why we can't derive space and time from experience? Because we need them to even be able to experience. Now my question is: why Kant infers from this that is our cognitive apparatus aplying space and time to the world? Why does he exclude the possibility that the world has this spatial and temporal structure and for that reason we're able to experience it? Certainly from the fact that space and time are necessary conditions for sensibility we cannot infer that the world doesn't have a spatial/temporal structure. So why Kant infers from that that we are the ones applying space and time to the world?

Thanks for your attention.