If you use a c clamp to push the piston in... and don't open the bleeder, you push the dirty fluid back to the master cylinder and take the chance of dirty fluid doing damage to the master cylinder... .
You also need to inspect the boot between the piston and caliper... if this is loose or torn, dirt can get behind the boot causing it to jam, not release and excessive wear will result as well as issues with the piston going back... .
The correct way is to open the bleeder, compress the piston and install the new pads... . install the caliper on the rotor and lock it down... . close the bleeder and now bleed the system making sure that fresh fluid pushes out the old fluid... I use about a pint of fluid each time I change pads to make sure that fresh fluid is in the caliper... . BTW - old fluid can hold water or moisture and later boil causing a soft pedal when you don't care to have it that way...
To answer you question I can only assume that if you can't get the caliper over the rotor with new pads is that you don't have the piston fully compressed... .
Hope this has helped...