The last large land mass discovered is a 37,000 km^2 archipelago north of mainland Russia called Severnaya Zemlya. It was discovered in 1913, but the four major islands weren't mapped until 1931.

There are no records of it before this time, and no evidence on any of the islands that humans had previously been there. It's considered to be a polar desert, but there are a number of plants and animals there--mostly birds and lemmings.

In the 1970's US satellite imagery was detailed and complete enough to confirm that there are no more undiscovered large land masses. In 1976 these satellites did discover an island a little over 1km^2 off the northeast coast of Canada.

Source: The Geographical Journal, Vol. 141, No. 1 (March, 1975), pp. 59-71

Hi there OP, you may be interested in this section from our FAQ that covers the history of cartography and mapping: https://www.reddit.com/r/AskHistorians/wiki/maps#wiki_history_of_cartography

Hi there to everyone else:

In this thread, there have been a large number of incorrect, speculative, or otherwise disallowed comments, including many asking about the deleted comments, which merely compounds the issue. As such, they were removed by the mod-team. Please, before you attempt to answer the question, keep in mind our rules concerning in-depth and comprehensive responses. Answers that do not meet the standards we ask for will be removed, and posters who break the rules of the subreddit admonished as applicable.

This thread is trending high in the subreddit, but those upvotes represent interest in the question itself, and it can often take time for a good answer to be written. We know that it can be frustrating to come in here from your front page and see only [removed] and this post, but we ask for your patience and understanding. If you are looking for some interesting content in the mean time, we hope you will check out our Twitter, the Sunday Digest, or the Monthly "Best Of" feature. It is very rare that a decent answer doesn't result in due time, so please do come check into the thread in a few hours. A Private Message to the Remind Me bot is a good way to remember.

Additionally, it is unfair to the OP to further derail this thread with off topic conversation, so if anyone has further questions or concerns, I would ask that they be directed to modmail, or a META thread. Thank you!

I think you may actually be asking several separate questions here, as mapping the Earth is ongoing process, and there are several points of completion depending on what you mean by "Skull Island-ish landmasses". As I understand, people were pretty certain there weren't any more hidden continents around after the discovery of Antarctica in the 19th century, but I'll let a 19th century historian comment on that.

If, however, you mean something more along the lines of "when was the whole Earth's surface effectively mapped such that there's no place large enough for King Kong to live in that's still unknown" then I can provide some insight as this is very close to my area of expertise.

To start:

GPS?

GPS, or any GNSS (Global Navigation Satellite System; a term that is inclusive of other constellations like GLONASS, Galileo, Beidou, etc.) itself is not a cartographic tool, but rather a navigational aid. GNSS provides two things only: position and time. Without a map of some sort to reference to, that position is not meaningful.

What's more relevant is the use of satellites to map the Earth's surface, which takes various form, but began principally with Earth-imaging satellites starting in the late 1950's/early 1960's. Early applications were limited, for a number of reasons, but mostly for the same reasons that early applications of any space technology were quite limited: cost and technology limitations couple with the priority placed on national security and prestige over practical space operations.

The "revolution" in Earth imaging came with the start of the Landsat program in the 70s. Though we now know about some military/intelligence satellites used for extensive imaging, such as the Hexagon program, these were intended for spying on military assets and the like, and not for cartographic research. Landsat-1 (originally Earth Resources Technology Satellite (ERTS) when the whole program was still ERTS), launched in 1972, was effectively the first dedicated imaging satellite for civilian use. The launch of Landsat-1 basically marked the beginning of the satellite imaging "era", which has currently culminated in everyone being able to see their backyards from space with a few clicks on google.

Landsat-1 was notably an optical imaging mission, since synthetic aperture RADAR (SAR) technology was still being developed. SAR data is generally more useful for cartographic purposes as it provides information on the height and shape of the land being illuminated much better than optical sensors. The creatively-named Seasat, launched in 1978, was the first SAR mission in space (that we know of, of course), and was tasked with observing ocean behavior. Seasat unfortunately didn't last very long, but nonetheless made a huge contribution to oceanography and more importantly, to SAR technology which has since been used extensively for Earth surface mapping and remote sensing.

Landsat-1 in particular was noted for discovering a tiny, previously unknown island off the Canadian coast, which to this day bears the name "Landsat Island". Whilst I don't know when cartographers felt completely settled as to the shape of the Earth-- and in fact I'm rather sure they don't-- in the simplest terms it was pretty clear at this point that there were no major landmasses of any appreciable size still out there waiting to be found.

There's an awful lot more very interesting stuff that could be said about more recent explorations, particularly in mapping the gravity field and density of the planet, but this would all be in violation of the 20 year rule so I'll leave it at that.