Possible to Push Eyeball Back During a Blepharoplasty?

Pushing on an eyeball will not cause it to be asymmetric.

However, surgery on the lower eyelid can either bring out an existing asymmetry (the more forward set eyeball will appear even more forward set if the same procedure on the lower eyelid is done on each side without compensating for the existing asymmetry.

It is possible to camouflage orbital dystopia of this type by selective cheeklifts.

The eyelid position should not move after routine lower lid blepharoplasty.  If too much fat was removed, it is possible for that eye to move backwards.  More likely, asymmetery seen after lower lid blepharoplasty can be the result of :

Preexisting asymmetry not detected by patient (look at before pictures)

Asymmetric removal of fat or skin

Photographs would be very helpful to understand what you are now experiencing after blepharoplasty.  It sounds like you are telling us that after eyelid surgery, your left eyelid is more ptotic or droopy after eyelid surgery.  This is a relatively common problem after eyelid surgery.  Your current eyelid surgeon may or may not be able to help address this concern.  However, one thing is for sure.  Your surgeon will be highly motivated to make you happy. I would recommend bringing your concern to the attention of your surgeon and getting their recommendations.  If necessary, consider a second opinion.