Can you knock out a small dent on a chrome bumper without cracking the chrome plating? This is a metal bumper, not plastic.

What vehicle? I would say in old school vehicles this more likely feasible. Newer trucks with thinner gauge metal are usually not repairable (at least not without a noticeable ripple).

Depends on your definition of "small" and "knock."

If by small you mean a shallow dent over a 2-3" area that is smooth with no sharp creases or gouges, then maybe.

And if by knock you mean gradually applying reverse pressure with a C-Clamp with a couple of pieces of wood between the clamp heads and the bumper, then maybe.

Anything beyond that, I would say if you were lucky enough that the plating didn't crack on the original impact you'd be tempting fate to try and smooth it out, and likely will end up with a bumper with smoother profile and an unsightly rust spot that will grow between the steel and plating.

But my wife's Kicks (Nissan) has plastic bumpers so I'm not familiar...

Looking at a '22 Ram 1500 with a chrome bumper. Shallow dent with no sharp crease (like door ding) about 2" across.
I have not purchased yet, just considering for my boys. The dealer offered to repair after the purchase. Trying to gauge how realistic that is.

Front or rear bumper? Is it in an area where the bumper is supposed to be straight, or is it in a curved section of the bumper like on the corner or upper/lower edge where it curves.

If it is in a straight section the dent can probably be worked out, but they will likely use metallic tools and a hammer. If it is in an inconspicuous area I'd probably ask for a discount and drive it with the dent. One of your buys is likely to do worse to it soon enough anyways.

If it really bugs you, ask yourself if you'd rather have a smooth contour with a rust spot bubbling up, or a slight dent and no rust.

Right on the top curve of the front bumper. Close to the front grill.

Then I would be skeptical they could work it out period, let alone do so without harming the integrity of the plating, but I'm not body shop guy.

I would ask to take the truck to an independent body shop and get an impartial opinion about it. If someone like Classic Doug says it's no big deal to work it out, then you know it can be done, but if a dealer sales guy or the dealer's own body shop guy are the ones says Ng it can be done then I wouldn't accept their opinion as fact.

You can usually buy cheap takeoffs on Facebook marketplace or Craigslist almost any day of the week. Find one for a decent price if the repair isn't up to your standards and replace it down the road.

Leave the ding and have them knock off a couple hundred.

If it is for your kid, they are going to dent it anyway.

I had a pretty deep angled dent on my F150 rear bumper. I took it to Ford and they straightened it out and you can't see it now. They did it as a favor or minimal cost after replacing my tailgate which was tore up.

But based on my experience i was surpised they were able to fix it.