This is perfectly possible to do...but there is a gotcha
D&D is an exceptions based game.
Specific beats General
(PHB page 7)
You need to have a rule to justify something exceptional. A place where people can walk and travel (explicitly) not having ground is exceptional.
The general rule is that the Border Ethereal is a mirror of the relevant plane:
Its “shores”, called the Border Ethereal, overlap the Material Plane and the Inner Planes, so that every location on those planes has a corresponding location on the Ethereal Plane.
(DMG page 48)
So, what is a location?
Oxford Dictionary defines location as
A particular place or position.
Next we ask what is a place?
Oxford Dictionary defines a place as:
A particular area on a larger surface.
Thus in order for there to be a "corresponding location" there has to be ground for that location as the originating plane has ground (the Material Plane, Feywild, Shadowfell, Elemental Planes all have ground).
Finally nothing in the DMG description of the Ethereal Plane, or Border Ethereal, states that there is no ground on the Ethereal Plane. As there is no specific rule removing ground from the Ethereal Plane, it has ground.
This means the first line of the spell
You cause a temple to shimmer into existence on ground you can see within range
The potential "gotcha" of the spell for your plan is this line (emphasis mine)
The temple is made from opaque magical force that extends into the Ethereal Plane, thus blocking ethereal travel into the temple’s interior.
As a result, unless you make the temple appear around you, you won't be able to enter your new Ethereal Temple while you are on the Ethereal Plane. The only way to enter your temple will be to go back to the bordering plane, go to a spot inside the temple and either cast "Etherealness" again, or "Plane Shift".
Aside: Dale M's answer relies on an interpretation of this line from the DMG:
[...] solid objects on the overlapped plane don’t hamper the movement of a creature in the Border Ethereal.
(DMG page 48)
that the ground is an Object.
The DMG defines an Object as:
For the purpose of these rules, an object is a discrete, inanimate item like a window, door, sword, book, table, chair, or stone, not a building or a vehicle that is composed of many other objects.
(DMG page 246)
Thus the ground is not an object for the purposes of the rules.