The "Climb onto a Larger Creature" action option in the Dungeon Master's Guide (p. 271) says:
If one creature wants to jump onto another creature, it can do so by grappling. [...]
As an alternative, a suitably large opponent can be treated as terrain for the purpose of jumping onto its back or clinging to a limb. After making any ability checks necessary to get into position and onto the larger creature, the smaller creature uses its action to make a Strength (Athletics) or Dexterity (Acrobatics) check contested by the target’s Dexterity (Acrobatics) check. If it wins the contest, the smaller creature successfully moves into the target creature’s space and clings to its body.
I think that dimension door or perhaps misty step would allow me to bypass the opposed Athletics/Acrobatics vs. Acrobatics check to place myself onto its back.
From there, it can use its action to shake me off (or whatever the DM can come up with). but mostly I'm curious about rulings for teleporting onto a creature. Certainly the place it is is occupied, but I'm not trying to land there.
Can I use the dimension door spell to teleport onto the back of, say, an ancient green dragon?