Mdthbs

I'm trying to explain a large continent-sized archipelago that doesn't run in any particular direction. As such, plate tectonics cannot possibly explain its existence. This is an Earth-like planet.

Would it be possible for a gigantic lake surrounded by land to be higher than sea level? Or would the pressure exerted by that much water destroy any land trying to keep it in?

If it is possible, then maybe the land suddenly collapsed in an area like a broken dam, draining the water from the higher-than-sea-level lake, which in turn revealed several landmasses that were scattered underneath the water?

Timescale could be anywhere from thousands to millions of years.

Good answers will tell me if what I am suggesting is possible, and if not, try to help devise a possible explanation for the archipelago shown in the following image:

The archipelago in question is in the top left of this image, between the upper halves of the leftmost and center landmasses.

EDIT: I'm talking about an elevation difference of hundreds of meters or more, a scale large enough to cause hundreds of large landmasses to be uncovered, should the water levels find a way to balance themselves.

Absolutely. During the Messinian Salinity Crisis the 'sea level' in the Mediterranean Sea was THOUSANDS of meters lower than that of the Atlantic ocean, for thousands of years.

The important thing for your example is that there would need to be a large enough surrounding drainage area to keep sea level in your archipelago stable relative to evaporation. Having it further north or south (e.g. not in the tropics) would help with this by reducing solar-driven evaporation.

There are parts of Earth's oceans, never mind landlocked sea-size lakes, that have differing sea levels.

The Atlantic and Pacific differ by a couple meters, as measured from the center of the earth -- this is measurable across the Strait of Magellan (off the Cape of Good Hope at the tip of Tierra del Fuego). There is a constant current in the Bosporus where the waters of the Black Sea (larger than all five Great Lakes combined) flow into the Mediterranean.

Trivially, if you have two seas that are cut off from one another by land, their levels will be set independently by the balance of inflow and evaporation (or underground outflow) in each. If one gets a lot of rain in its watershed, while the other largely borders an arid region, the rainy one will tend to be higher. For connected bodies, the limitation is how fast water can flow from the higher to the lower, relative to how fast water flows into the higher. Hydrodynamically this is a general condition -- regardless of the size of the bodies.

Not an original starting point, I recognize it, but Randall Munroe already covered this answer in one of his What if.

What you see above here is how Earth would look like once you drained the oceans (and made the Netherlands much bigger).

To use Randall's words:

There's a surprising amount of water left, although much of it consists of very shallow seas, with a few trenches where the water is as deep as four or five kilometers.

On our present Earth we have mountain lakes which are kilometers above the sea level. Usually the problem with the rock bed resistance is given by the profile of the rocks which becomes thinner as the water rise and at the end cannot contain it. Else the bottom is capable of resisting the pressure: any depth of water is always going to weight less than the same height of rock (except for pumice), thus if the bulk rock can withstand its weight, even more can withstand a lake/sea above it.

The Great Lakes, Lake Baikal, the Caspian Sea, and the Dead Sea are all reasonably large bodies of water that are not at global sea level.

The Great Lakes are hundreds of feet above the global sea level.

The Dead Sea is not very large, but it is relatively close to the Mediterranean and Red Seas.

An example: the Pannonian Sea

The Pannonian Sea was an inland sea which existed for about 10 million years; during the last part of its existence it was isolated from the ocean. It covered most of the territory of modern country of Hungary, and large parts iof Croatia, Serbia and Romania. I would say that this qualifies as a "very large lake".

The Pannonian Sea during the Miocene Epoch, about 6 million years ago. The lake was about 500 km (300 miles) across. Map by user Panonian, available on Wikimedia under the Creative Commons CC0 1.0 Universal Public Domain Dedication.

Hawaiian style!

https://www.marinebio.net/marinescience/02ocean/hwgeo.htm

Hawaii is geologically a unique place on Earth because it is caused by
a 'hot spot.' Most islands are found at tectonic plate boundaries
either from spreading centers (like Iceland) or from subduction zones
(like the Aleutian Islands). There are few 'hot spots' on Earth and
the one under Hawaii is right in the middle of one of the largest
crustal plates on Earth - the Pacific Plate. A geologic 'hot spot' is
an area in the middle of a crustal plate where volcanism occurs. It is
easy to geologically explain the volcanism at plate spreading centers
and subduction zones but not as easy to explain a 'hot spot.' The
molten magma breaks through the crustal plate (theories describe this
as either from a weak/thin part of the plate or a particularly hot
part of the molten magma)... If
the hot spot is under the seafloor (as it is in Hawaii) it produces
undersea volcanoes. Some of these volcanoes build up to the surface of
the ocean and become islands. Over millions of years the plate may
move across the 'hot spot' and the original volcano become extinct but
a new volcano will begin to form in the area of the 'hot spot.'

Your archipelago cannot be explained by plate tectonics; neither can the Hawaiian archipelago. You have a hot spot. Those islands are all volcanoes. They are tall, some of them. The hot spot has moved around, creating new volcanic islands as it did.