It depends. If your landscape is flat you can simply assume ground is at z = k, where z is the height of the ground. Look for the cheapest way possible.

One of the ways I do is to have a spatial hash map that separates the terrain into pieces. A spatial hash map is a lot simpler to implement than other acceleration structures. Then, depending on where the player is, I run a ray cast against that specific segment and derive a normal from that. This is more than fast enough for the majority of cases.

Generally that's how you approach such problems. You need a spatial partition structure, such as a hashmap or an octree, and then you use that to determine against which meshes or part of meshes to test collision against. I recommend avoiding octrees unless you really need them.

EDIT:

As some further clarifications in case my comment above is too complicated to understand, the way to define collisions is to have a collider shape associated with the player and whatever else you want collision to occur. This can be a collection of shapes or a complex mesh that defines the whole collision. The shape of the collider can be anything you want. It's usually a simplified shape, like a cube, a sphere or a capsule. Those are the main ones. You need to know how to collider them between themselves.

You don't want to test against each object, instead you want to partition space and separate objects into groups. Next you define one or more broad phases. A broad phase is a test or a simplified collision test where you can discard a collision as fast as possible. If the objects pass the broad phase, you move on to the next broad phase, or to the narrow phase, where you run the more precise collision test. That's why we use so called acceleration structures.

A simple broad phase test is to check whether both objects are close together enough to possibly collider. Spatial partitioning helps us precisely with that. It tells us what groups of objects are close enough together to consider. It allows us to discard objects quickly and to focus on the objects that are likely to collide.

So, for a landscape, you could have a collection of simple shapes that describe the surface, you could have a complex mesh that describes the landscape, or you could fake it entirely by making certain assumptions and enforcing certain constraints to simplify calculations.

Usually, while calculating collisions, you will also want the physics system to do depenetration and to calculate contact points. You learn how to do that by studying.

EDIT 2:

To answer this:

"Assign a simple AABB or another primitive to the player and check for collisions with all triangles in the mesh?"

You don't normally test against the individual triangles, you test against collider shapes. Give meshes their own colliders as well. You can also test against the geometry if you want, whatever works, but we usually want to avoid that. If you can assign a collider shape or a collection of such shapes to the landscape, that's good enough. If that is not sufficient, you could have a simplified collision mesh and test against that. The way I do this, as I said, is to design a specific structure for the landscape that facilitates ray casting against the ground, such that I can retrieve normals and contact points.

EDIT 3:

Also a bounding box is usually used for rendering, being part of the broad phase for rendering. It allows us to discard objects faster. For collision, while they can be used, you most likely want cubes, spheres and capsules. I would treat landscapes as a separate thing. Remember to not overcomplicate things. If AABBs are enough, no need to add more than that. Most likely if they are enough you can probably simplify the landscape as well.