Bhagwan Shiva is transcendental, he is the Ultimate Consciousness which is static and eternal. He was there even before creation, it is there during the functioning of this creation and when the creation would dissolve, he will still be there.
Now particularly the Mount Kailash that we see in our material realm with our eyes, it is the reflection of the Ultimate Abode of Shiva which is the Original Kailash (Shivaloka).
It is stated that when Brahma was performing the task of creation, he was facing a lot of challenges and he got frustrated because his creation was not able to control the living beings. In order to help Brahma in the creation, Shiva himself incarnated to control the beings in material realm by taking the role of destroyer.
This particular manifestation of Shiva is known as Rudra, the complete incarnation of Mahadev. He resides at Mount Kailash because of Kubera’s penance. Kuber is the devotee of Shiva and his very dear friend and so Shiva as Rudra emerged from his own heart and manifested in material creation through Brahma’s forehead, went and settled at Mount Kailash because of Kubera's devotion.
Hence, Shiva being eternal reality and present before creation, during and after it, he stays on Mount Kailash because of the penance done by Devtas, not only Kubera but also the creator Brahma himself. Shiva is omnipresent, so he is there in his Supreme abode of Kailash (the spiritual realm beyond the Mount Kailash and Universe). The same Shiva also resides in Kashi abode eternally in the form of Mahesh or Maheshwar (Vishveshwar).
There are multiple lokas and residences of Shiva for his different manifestations. As Bhairava, he lives in cremation grounds.
So his presence is everywhere, not just the spiritual abode but within the material realm also otherwise it cannot function at all. The Kailash we see from our eyes is one of the many places associated with one of the many forms of Shiva.
Har Har Mahadev 🙏