I'm reposting the same answer that I made to this related question as it is the only solution I am aware of.
Find an ether cyclone
The details of the Ethereal Plane are described in the Dungeon Master's Guide in the section "Creating a Multiverse". There are two regions of the Ethereal Plane, the Border Ethereal which is connected to the inner plane you traveled there from (via blink, etherealness, etc.), and the Deep Ethereal, which can only be reached by:
a plane shift spell or ... by means of a gate spell or magical portal
The Deep Ethereal is then connected to each of the Border Ethereal regions by magic curtains:
Scattered throughout the plane are curtains of vaporous color, and passing through a curtain leads a traveler to a region of the Border Ethereal connected to a specific Inner Plane, the Material Plane, the Feywild, or the Shadowfell.
So you could travel from the Deep Ethereal to any of the Border Ethereal regions, but that doesn't get you out of the Ethereal Plane.
However, there is another tidbit in the Dungeon Master's Guide:
An ether cyclone is a serpentine column that spins through the plane. The cyclone appears abruptly, distorting and uprooting ethereal forms in its path and carrying the debris for leagues.
One of he effects of these cyclones is for
all creatures in the vicinity [to be] [h]urled into the Astral Plane
There is only a 1 in 20 chance that any given cyclone has this effect, but eventually finding one is your escape from the Ethereal Plane.
Once in the Astral Plane, there is an abundance of portals that can take you where you need to go:
Gateways leading from the Astral Plane to other planes appear as two-dimensional pools of rippling colors, 1d6 × 10 feet in diameter. Traveling to another plane requires locating a color pool that leads to the desired plane. These gateways to other planes can be identified by color, as shown on the Astral Color Pools table. Finding the right color pool is a matter of chance: locating the correct one takes 1d4 × 10 hours of travel.
However, among the planes these color pools can lead, some are missing; these being:
- the four Elemental Planes
- the Feywild
- the Shadowfell
You could instead find a color pool to the Outlands (which are a leather brown color) and make your way to Sigil which is a:
bustling planar metropolis [that] holds countless portals to other planes and worlds.
Alternatively, there are denizens, specifically the Gith, of the Astral Plane who have access to planar magic, and you could negotiate with them for passage to a plane of your choosing. More about their planar magic can be found in Mordenkainen's Tome of Foes.
If this is the path you take, many elements of the adventure would involve the Planescape setting. While this has yet to be incorporated in 5th edition, there are a lot of interesting and fun characters and societies in this setting that your GM may want to pull from.