Quality compositions / studies are like that. It's considered bad to make the first move something obvious like a capture or check.
I don't know of any collections, sorry.
Although forcing moves (like captures and checks) are absolutely mandatory to calculate in a real game. So maybe hold off on purposefully ignoring them until later. That sort of training seems useful only if you already habitually calculate at all captures and checks.
I have recently read an old Wei Yi interview where he mentioned that one of the ways the Chinese coaches used to train their students was giving them mate puzzles where the first move of the solution was never a check. Does anyone know of any existing collections or a way to retrieve such puzzles from a database?