It’s important not to trap dust and other particles behind the glass while framing. The best way to avoid this scenario is to wipe all components down with a lint-free rag, or even a cloth diaper rag. The point is to dust all surfaces before removing the backing from the plexiglass, for example.
You want to plan and place everything such that you can assemble the mat, backing, glass or plexiglass, and frame together in the proper order as quickly as possible. Combine the glass or plexiglass first with the mat, which already has the artwork attached, add the backing board, and then check to see whether there are any dust particles trapped in between.
If there are, then do another pass at dusting off all of the components, or if it’s in a corner where you can easily reach, place the rag in between the glass or plexiglass and the mat and force the dust particle out. Once it passes inspection, add the frame and secure the mat and backing board with metal offsets for a wood frame or spring clips for a metal frame.