Yup! Elevators are entirely possible on the server, without using any Redstone at all!

How to make elevators?

The following materials and steps are based on an elevator linking two floors only.
You will need:
  1. 1.
    1 Iron Block
  2. 2.
    1 Glass Block
  3. 3.
    2 Signs
  4. 4.
    2 Buttons
You can use any color for the glass block!
You can use any wood for the signs!
You can use any block for the buttons!

1- Place an iron block on the ground floor like this picture:

You cannot have any iron blocks that are not part of the elevator touching the iron block(s) of the elevator whatsoever.

2- Place any button a block behind and above the iron block just like the picture. Then, place an empty sign right above the button.

If you want to make it clearer, simply write the floor name on the second line of the sign.
Here, the sign says 'Ground Floor', which will be the name of this floor.

3- Place a glass block on the second floor, just like the following picture.

You cannot have any glass blocks that are not part of the elevator touching the glass block(s) of the elevator whatsoever.

4- Moving on to the second floor, replicate step 2 and on this floor. You can replicate step 3 here only if there is an additional floor above it.

Here, the second sign says 'First Floor', which is the name of the floor.

5- Finally, right-click the signs once on each floor with an empty hand.

Max Size of an elevator:

If you want to have more than 2 floors, simply replicate step 4 and step 5 on every floor above the first floor ( the floor with the iron block )
When there is more than one floor, right-click the sign to alternate between floor destinations.

If you named it in the above steps, you can alternate between the floor names, but if you did not name it, you will only be alternating between the floor numbers.

You can ONLY cover the iron block/glass blocks of the elevator with any carpet and nothing else.
If the elevator is larger, you can put more signs and buttons on other sides, as long as there is signs and buttons vertically above it all the way up.
Make sure that there is nothing between the iron block and the glass of the elevator. The glass of the elevator must be as wide as the iron block of the first floor.