I’m trying to identify a short story my dad read to me as a child. He said it was from a compilation of short stories around the theme apocalypse and time-travel. The plot line is something about scientists that find a way to send things back and forth between the present and the future. The story ends with a small statue of a cockroach in a plumber's outfit coming through the machine.
"The Figure", a short story by Edward Grendon (pseudonym of Lawrence LeShan), first published in Astounding Science Fiction, July 1947, available at the Internet Archive. If your dad read it in an anthology of time-travel stories, it was probably Travels Through Time, a 1981 hardcover edited by Isaac Asimov, Martin H. Greenberg, and Charles G. Waugh.
How far in the future our gadget would operate we had no way of knowing. Lasker said he would not even attempt to estimate "when" the field was active. When the power was turned off, anything that was in the cube of forces would be brought back to the present space-time. In other words, we had a "grab" that would reach out and drag something back from the future.
[. . . .]
The figure on top is standing up very straight and looking upwards. It's dressed only in a wide belt from which a pouch hangs on one side and a flat square box on the other. It looks intelligent and is obviously representing either aspiration or a religious theme, or maybe both. You can sense the dreams and ideals of the figure and the obvious sympathy and understanding of the artist with them. Lasker says he thinks the statue is an expression of religious feeling. Dettner and I both think it represents aspirations: Per adra ad astra or something of the sort. It's a majestic figure and it's easy to respond to it emphatically with a sort of "upward and onward" feeling. There is only one thing wrong. The figure is that of a beetle.