You don't mention the rough dimensions of the piece, or whether it is hard or soft or in-between.
It's possible, of course. This was how wood was brought into the shop and then resawn or already rough sawn. There is a whole practice of preparing stock for actual use with hand tools.
As you've noticed, sandpaper is not the right tool. Sandpaper isn't for removing lots of material, unless it is for contouring on a spindle sander. Certainly not the right (hand) tool for flattening a surface. Not only is it slow and messy, it isn't very good at giving you any reasonable flatness.
A plane is what you want to use. Ideally, you want the equivalent of a #4 to #5 plane. Since we don't know what wood or tools you have the best advice is to start removing material across or along the board. You start with very light passes, adjusting the depth until you are taking decent ribbons of wood off the surface. It is fine to just skip over the hollows at first -- the act of planing a surface is about taking all the high spots down, really.
You shouldn't have to be jamming hard on the plane; it should be a relatively regular and smooth action. If you find yourself digging in and tearing wood out, back the depth off. If the problem persists, resharpen or adjust the blade.
There is variety of plane called a "scrub" intended for removing lots of material fast, which is basically a shorter "jack" plane that allows you to get into some of the hollows, often coupled with a profiled or notched blade that removes material fast. You'd follow this up with a more careful smoothing pass with a flatter, longer plane. But there is no requirement that a scrub plane be purchased or used (but check if you have a tool lending "library" in your area) as any middle-sized plane can work with a little patience.
Otherwise, the blade should be sharp. Like, "pass through paper easily, shave the hair on your arms" sharp.
For removing a lot of wood, if you have a plane with an adjustable mouth (i.e., you can change how narrow the blade slot is) it should be a bit wider than for smoothing or finishing work. Sight down the sole of the plane and make sure the same amount of blade is poking out along the width.
Take care to note whether your plane is intended for bevel-up or bevel-down operation. Most planes will be bevel-down, unless you have a low-angle plane of some sort.
Remember that you push with your body, not your arms, which should remain in the relatively same position relative to your body and the tool. The idea is nice even force across the material without removing or lifting the sole from the work at the end. Drag it back, reposition, and go for another overlapping stroke.
This is one of those cases where visiting many of the YouTube channels on hand tools will show you better than we can tell you.