First of all it would probably collapse on Earth. Mars only has 38% gravity which allows taller structures. However lets ignore that for the moment,

Olympus Mons is about 25 km (72,000 feet) tall. That is about 2.5 times Everest. It is also so high up that not only can’t you breathe, it is starting to push body limits on withstanding low pressure. I think at a minimum you would need a pressure suit and LOTS of oxygen.

In fact it would require so much oxygen that you couldn’t possibly carry it up. The only possibility would be for you to somehow parachute oxygen tanks onto the route ahead of time and then use all of those. However, most aircraft can’t even fly that high.

That would require something like military aircraft to get that high. I won’t say it is impossible but it would be a logistical nightmare and cost many millions of dollars.

It is also about -55 C half way up, so you better have cold weather gear.

There is also the sheer distance issue. After scaling the initial cliffs that are kilometers high (think 4 or 5 El Capitans on top of each other) you have hundreds of kilometers of uphill slope. Below is Olympus Mons laid over France.

Just an update note. The slopes are about 5–10 percent grade on top depending on which side you come from, so it isn’t gentle on the top but it isn’t climbing either. It is walking uphill. The cliffs on the edge however are about 4 km (2.5 miles) high. That is because when it was formed it was sitting in a 4 km deep ocean and at the edges the lava cooled and fell to the bottom. It is a couple of billion year old feature from a time when Mars was wet and volcanic. It is the largest volcano in the solar system.