Procedure to Make Eyes Bigger Other Than Eyelid Surgery?

Dear Sesameseed
Please recognize that some surgical maneuvers are safer than others. Creating a double fold will make a very big difference for you. In Singapore, you could have your eyelids threaded to create a double fold. While this procedure is seldom permanent, it will help you understand how a fold will change your appearance. If you like the result, you can consider cutting surgery once the threads fail.
Surgery on the epicanthal folds is another matter. This would make the eyes look wider. This is what is done to take an inside fold to an outside fold. However, there is a real risk that you will be left with visible scars in the inner corners of the upper eyelid. For this reason, I generally advise against this type of surgery.

Other than eyelid blepharoplasty surgery, there is no other way to make the eyes bigger. The creases can be made deeper by removal of fat and muscle to create more of a fold to the Asian eyelid.

It appears that you have hanging of the eyelid skin that can be reduced by a double eyelid surgery or perhaps by a brow lift. In addition, the medial hooding or epicanthal fold is in part due to excess skin across the root of the nose from inner eyelid to inner eyelid. If you pinch the skin between the eyes near the bony root of the nose, you should see the eye aperture open up. If you have a relatively flat nasal bridge, a nasal implant to raise the bridge might help to take up this skin slack. The surgeries to remove the epicanthal folds tend to require excessive scars.

Yes, there are other procedures for making eyelids bigger other than plastic surgery. You don't even need to see a plastic surgeon or cosmetic specialist.
Tape applied on the upper eyelid can create a crease (double eyelid). Glue applied with a plastic applicator is another alternative temporary solution. Based on the size, shape, and exact location of where the tape or glue is applied, various subtle eyelid creases can be created (wide, narrow, oval, etc).
However, only plastic surgery of the upper eyelid in Asian blepharoplasty will create a long-lasting solution. Speak with a plastic surgeon performing eyelid surgery to see if Asian blepharoplasty is appropriate for you. Best of luck.