How do polish acrylic (PMMA) plastic to a glass-like shine? If you use fine-grit sandpaper, you can improve the shininess of acrylic quite a bit, but to get a glass-like shine, you must use careful technique with a propane torch. Quickly pass a propane torch from edge-to-edge of the acrylic taking care not to melt or burn your material, or else it will be ruined. See the wikihow article for full details.
20191103/DuckDuckGo how to polish acrylic
20191103/https://www.wikihow.com/Polish-Acrylic
So, armed with knowledge of this technique, you can proceed to finish 3D printed acrylic parts, provided that you have good solid formation in the middle of the material. 100% infill, without interior layering boundaries.
Please note that pure acrylic plastic is brittle and scratches/chips more easily than glass, so your shined material is vulnerable to damage and you may feel the need to re-shine in the future. You may consider using other plastics that are tougher but come at the expense of less shine.
20191103/https://en.wikipedia.org/wiki/Poly%28methyl_methacrylate%29