Surgery to push eyes forward?

It's hard to answer this question without seeing a photograph. Facial balance and harmony as a whole tend to make the eyes appear larger. This is why after a rhinoplasty, brow lift, or eyelid surgery the eyes often look larger even though they are the same size as they were before surgery. Common things to be careful of that may make your eyes look smaller are overuse of filler in the cheek and around the eyes, as well as eyelash serums that contain prostaglandins. I'd recommend seeing a local Facial Plastic Surgeon, Oculoplastic Surgeon, or Plastic Surgeon for further evaluation to see what can be done to help you achieve your goals.

Oculoplastic surgeons can treat both Enophthalmos and exophthalmos. Training for these procedures is included in plastic surgery, training and facial plastic surgery training as well but not all plastic surgeons do these procedures on a regular basis.
Whether the procedure is appropriate or not, maybe another story.
In regards to providers who have experience with eyeball positioning surgery. You may do better consulting with oculoplastic surgery.
Best,
Mats hagstrom MD