A traditional way of applying a silver coating to glass is through a chemical reaction using a reagent known as Tollens' Reagent. This reagent is prepared from silver nitrate as the source of silver.
Depending upon the surface chemistry of your cured SLA polymer, it may be possible to coat the polymer directly, as one would coat glass. There may also be a coating that will adhere to the SLA polymer and serve as a surface primer to which the silver from the Tollens' Reagent will adhere.
My recommendation would be first to identify the specific SLA resin that you will be using. This information should be available on the container, its packaging, or a Material Safety Data Sheet (MSDS).
Some research, such as an internet search, may provide additional information once the polymer chemistry is known. You might also find some helpful information from the SLA resin or printer manufacturer in the form of "Application Notes" that address applying surface coatings to SLA 3D-printed components.
I recommend performing a small-scale test to see what the Tollens' Reagent reaction does on the surface of a 3D-printed part that is made from the same resin that you will use. You might also experiment with different resins. Several resins may work equally well for forming your part while one provides a better surface for applying a mirror coating.
It will be necessary to apply a protective coating to the silvered surface, once prepared, to prevent oxidation.