Could it be possible? Yes, but it is up to you, the DM.
Assuming a magic world, there are many ways to search for this object, for example by narrowing the search area by using some divination spells. Other answers (see here and here) provided details for employing such spells.
In addition to divination magic, one may summon creatures for searching and retrieving the gem: for example, Summon Elemental is one of the best choices (details are below).
There are several strategies for finding the gem: the fact that it has not been found yet is completely up to you. For example, the gem is considered a message from the gods from underwater people (e.g., Merfolks or Sea Elves) and it is heavily guarded and/or hidden from divination magic. Or the meteor has landed in the ocean near a dead-magic-zone1, where divination magic is ineffective and where summoned creatures cannot enter, or in a zone where magic has wild effects2, where any magic could have bizzarre and/or unpredictable results.
Another possibility is that the meteor has landed in a particular zone of the ocean, but during the centuries strong underwater currents eroded it and made the gem travels for mile: people have been searched for this gem in the wrong place.
Summing up, if your story needs that the gem is a legendary item that has not still been found, you can come up with several reasonable settings, which can be also heavily involved in the quests/campaign for the search, if you will.
Down below a short list of strategies for searching and for retrieving the gem is provided, beside the divination approach listed by other users.
Be (or hire) a druid.
Another way to search for the item is to be (at least) a 4th level druid that had seen a Dolphin (or another beast with swimming speed): in this way the druid can search the area and find the location of the gem. In case the subclass is the Circle of the Moon, there is no CR restriction.
When the druid can wildshape into a Giant Octopus, they could be able also to retrieve the gem, using the tentacles.
The drawback of this approach is the depth at which the gem is. For example, if the gem is at more than 500 meters deep, in real world dolphin cannot reach it. This approach could be of some use in case the gem is "close" to the surface, or to spot unusual location in the search area from far away. About Giant Octopus, this is up to the DM.
The DMG provides some rules about underwater pressure:
Swimming through deep water is similar to traveling at high altitudes, because of the water's pressure and cold temperature. For a creature without a swimming speed, each hour spent swimming at a depth greater than 100 feet counts as 2 hours for the purpose of determining exhaustion. Swimming for an hour at a depth greater than 200 feet counts as 4 hours.
For depths as the ones depicted in the answer, the DM has to decide if the above rules still hold or if more dangerous arise, or they can decide to adopt and adapt the optional rules from Ghost Of Saltmarsh:
OPTIONAL RULE: PRESSURE AND OBJECTS
With this optional rule, characters who dive deep in
the ocean require specialized equipment that can withstand the ocean's pressure. Nonmagical objects not made to withstand the water pressure are destroyed at various depths, as determined by the material used to create them. This destructive depth is presented for various materials on the Objects and Water Pressure table. Objects made of other materials break at the DM's discretion.
| Material |
Destructive Depth |
| Glass. crystal, ice |
100 ft. |
| Wood, bone |
500 ft. |
| Stone |
1,000 ft. |
| Iron, steel |
1500 ft. |
| Mithral |
2,000 ft. |
| Adamantine |
2,500 ft. |
Another possibility is to borrow the rules from Storm King's Thunder3, chapter 10, page 202, when the Maelstrom is described:
Maelstrom lies on the floor of the Trackless Sea, nearly 3,000 feet beneath the surface.
[...]
Creatures and vehicles at Maelstrom's depth take 7 (2d6) bludgeoning damage per minute from water pressure unless they are adapted or built to withstand this environment. [...]
A spell that allows one to breathe underwater provides no protection against the crushing effect of water pressure unless the spell's description says otherwise.
In case of a Circle of the Moon Druid4, at 10th level one can wildshape in a Water Elemental: this make the search more easy.
One can interact with marine beasts, using Speak with Animals.
The Speak with Animals spell allows to, well, speak with animals: intelligent creatures such as dolphin can be employed for such task, making them explore the area for you and report where the gem is. Moreover, if the gem is not stuck anywhere, the caster can instruct the creature(s) to retrieve it for them:
You might be able to persuade a beast to perform a small favor for you, at the GM's discretion.
All the limitations about pressure and depth are still to be considered.
Summon creatures for doing the job for you.
A couple of spells can employed: Summon Beast, for summoning a marine beast, and Summon Elemental, with the natural choice of water. The caster can instruct the creatures for searching and eventually retrieving the gem (in case of beasts, see the remarks in the previous section).
A remark about Water Breathing.
Water breathing allows to breath underwater, but at 5 kms (5000 meters) underwater, the pressure is around 501 atmospheres, deadly for normal humans.
1 Have a look at the box "The Weave of magic" in the PHB:
[...] the most powerful archmage can’t light a candle with magic in an area where the Weave has been torn.
See also the box Weave-Affecting Magic in The SCAG:
Dead Magic. In rare areas of dead magic, the Weave
is absent. Not only do spells and magic items cease to function, but even the supernatural abilities of creatures that are innately tied to the Weave might fail as the knot of the Weave they carry with them unravels.
2 See again the box Weave-Affecting Magic in The SCAG:
Wild Magic. In an area of wild magic , the Weave becomes "tangled," spontaneously forming its own constructs and resulting magic. It also tends to twist the constructs of the Weave created by spellcasting, causing unexpected results.
3 Credits to Peter Cordes that pointed this out in the comments.
4 Credits to Tollef that pointed this out in the comments.