Well, before anyone can go for an unknown alien pyramid at Mars' surface, you should have a lifting-system that can move the whole expedition over there.
Recently that Exo-Mars-Mission set up by the ESA was launched by a Roscosmos (russian) rocket because NASA doesn't have a system powerful enough to get something this big even close to Mars. If the poor guys there don't get any more funds by whoever will be elected as Mr (or Mrs) President, all you can afford for a pyramid exploration would be some small robot or a joint venture with other space agencies. If you want to have a full blown mars base staffed with living humans doing the exploration, you'll have to send at least a dozen missions to Mars, that all have to work out fine.
Yea... there was that movie/book about the guy who grows potatoes at Mars because they forget him. It did look like its easy to send a human exploration team to mars (and back, partially), but I never gasped where all the money necessary for this came from.
So if you want to have your exploration a single-country-one, everything that goes up would certainly show a bunch of ads... every big company would kill to be the first one to advertise to an alien species. The other option would be to have a joint venture; NASA, India, China, Japan, Europe (ESA), Russia (Roscosmos), and even Brasil all have some kind of space program. This is something the whole earth really should take part of.
As the others said: send a robot in. However you do not want to control it from Earth. It would be like a computer game with a lag of several minutes (citation needed). That guy in front of the screen would notice that his RC-car fell into a hole minutes after it happened.
So make it fully automatic (and make sure it does not paint human private parts at the interior walls), or alternatively already have an space base up there. Even a simple base in orbit would be a great help in terms of the ability to respond to the discovery. This way at least you do not have to explain where all the money grew from all this sudden. Even more - an existing base could produce a makeshift a robot on their own if necessary; If everything fails, go collect one of the mars-rovers and let the group-mechanic play with it.
But never ever would someone be allowed to send in a human. The only exception would be when the mean alien crawls out and kidnap the exploration teams females. But that is one of these tropes... "mars need woman" or whatever its name was.
So... my vote: you need to start with having a fully autonomous explorer robot crawling in (bring a fiber-optic line with you, because no one knows how the wlan will be inside the pyramid), or have some less advanced remote-controlled vehicle moving through while a human operator operates the controls from a fairly close proximity.
But beside... what its inside? alien mummies? :)
EDiT: I appreciate that someone looks over my typos, but whats up with the change of multiple (correctly written) words just because they are... i don't know? It feels not right if you discovered an error, hit edit and find sentences that differ in great detail from your original ones... strangely, the history says I did the changes... must be some kind of alien mummy telepathy ;)