Lord Mahadeva does really exist. He stays on Mount Kailash, which is currently present in Tibet. But for a normal human eye, Mount Kailash looks like just normal mountain.
The people well versed in Yoga can see divine Mount Kailash with Lord Mahadeva at that place. Just like how Parameswara always stays at Kasi, He also stays in human form as Rudra or Shankara on his abode at Mount Kailasa.
Skanda says one can see Divine abode (of Kaasi) with help of Yoga or meditation in Chapter 182 of Matsya Purana.
भूलोक नैव संयुक्तमन्तरिक्षे शिवालयम्। अयुक्तास्तु न पश्यन्ति युक्ताः
There the abode of Šiva (Šivālaya) is situated in the space. It is not
connected with the earth. Unworthy people, void of Yoga are not able
to see that abode; but the Yogins can realize it by their knowledge.
Just like Kasi, one can see Mount Kailash and Lord Shiva with help of Yoga. Not only Kasi and Kailasa, people well versed in Yogic techniques can see other subtle worlds or dimensions.
Sri M, a modern Yogi from Madanapalle, saw Lord Shiva at Mount Kailasa when sitting in meditation during Kailasa Manasa Sarovar Yatra. He mentioned his experience in his book Apprenticed to a Himalayan Master.
On the second day of the parikrama, having traversed the Dolmo La
pass, which is 18,500 feet above sea level, we reached the camping
site at around 8 pm. We were tired and exhausted, for, the oxygen
levels were very low, and we had walked twenty-two kilometres that day
over a really difficult tract.
After settling down in my tent, I instructed our friends not to
disturb me after dinner. Many of us suffered from nasal bleeding. I
wiped my nose clean, emptied my bladder near the rocks, and zipping
close the flap of the tent, sat in padmasana, my attention fixed on
the Ajna chakra. Blood rushed to my head and a streak of lightning
shot up my spine, and within seconds, I was out of my body clothed in
a blissful silvery sheath.
This new luminous I, passed swiftly through several planes where glorious beings dwelt, and reached the wondrous realm that glowed with
a silvery blue soothing light. Two large blue cobras guarded the patio
of a white crystal palace. They swung their hoods nodding to me to
enter. In the central hall, on a raised crimson couch was Mahadev,
the Great Being, manifested as the Luminous Void, changing every now
and then into the resplendent form of Shiv Bholenath with the crescent
moon on his head and a black cobra around his neck, his body snow
white, and his third eye looking like a blue pearl.
So, Lord Mahadeva really exists at Mount Kailsh and we just can't simply see Him with normal eyes.