How can we see objects with the help of light if we cannot see atoms?
As explained in a related previous thread, the human eye cannot resolve atoms (in the sense that visible light is too coarse to distinguish one atom from its neighbours in solids and liquids), but that does not mean that we cannot perceive the light that they emit.
The light emitted by each atom is generally quite faint (probably just under the detection threshold for human vision), but if the atom is emitting (or reflecting, or scattering) photons, there's a nonzero probability that the cells in the human eye will detect it.
If you then put a bunch of atoms together, they will emit more photons, and the probability that the cells in the eye will detect it increases. Put enough atoms together, and it becomes certain that the eye will detect the signal. We cannot tell with certainty where the signal comes from to any accuracy better than the wavelength of light, but that does not mean we cannot detect the signal.
This can probably be answered by analogy. If you look at an individual pixel on a TV screen it doesn't tell you much about what picture is on the screen. However, if you have a screen with several million pixels, when viewed together you are able to process them into a meaningful image.
The situation is similar with atoms. Your eyes do detect individual photons coming from atoms, however just like looking at a single pixel, seeing a single photon from a single atom would not even register on your vision.
It depends with what you mean with the word "seeing", because seems to me that you are confusing it with the word "resolve".
You cannot resolve the particulars of the atomic structure just with electromagnetic radiation, because higher wavelenght as you said are "too big" for the atoms; the human visible light has a wavelenght not too less than $1\mu$m, while the extension of a whole atom is in general around $0.1$nm. Theoretically you can go with higher frequency radiation, so less wavelenght, like X-rays or gamma radiation, but Nature is smarter and what happens with this energy scale of radiation is that it starts to actively interact with atomic structure and so, even in this case, you have a limit in your ability to resolve atomic structure.
But even if you have the most precise instrument in the world quantum mechanics states that the basic principle of Nature is indetermination, so it's very hard to say what you would actually "see", maybe like a substantially blurred picture if you just want to imagine it.
So in conclusion light interacts with atoms with absorption, reflection and diffraction, that's what allows you to perceive trough vision complex bodies; but at the same time, given the underteministic nature of the things in the World, doesn't allow you to resolve them with arbitrary precision.