If large, invisible particles exist, according to Epicurean physics, then they should still form compounds which can be seen. They could have reasoned that there are no compounds that, when broken, simply poof into an invisible realm of large particles. For example, there is not a mineral that can get split in half, and then both halves suddenly disappear. Everything we observe seems to dissolve, eventually, into something that is at least finer than dust.
That's a good point. Is it possible that this is what Epicurus meant? By atoms so large they fall within our ken, he might not have meant seeing the atoms themselves floating around like balls but more like things being more granular than we normally see.
Or being experienced by touch as stated above.