Visualize the standard push-up, being done from the side, with emphasis on the big toe joint.,
Note that base of the big toe is bent, in the the push-up position and that extension of the big toe joint can be reduced by your ankle joint dorsiflexing.
Before doing push-ups (and push-up type of exercises), warm-up and do a calf stretching exercise.
Visualize again the side view of a push-up being done, and realize that a “ram rod” straight body line puts less strain, to the base of your big toe, base joint than a sagging one.,
Have in your regular stretching routine and before doing push-ups, a hamstring stretch or two.,
Do your push-ups, and push-ups type of exercises, on carpet, a mat, on grass and best of all on sand.
Finally, exercise the muscles of your foot:
The top of your foot with manual resistance or isometrically.
,,, When doing push-ups, keep your body straight or in a slightly above straight position.
, A supple hamstring will allow you to keep your legs straight.
The underside of your foot, by picking up a towel or fabric.