Subordinating (masdari) particle

أَنْ تَصُومُوا (“that you fast”) can be re-read as one noun: صِيَامُكُمْ (“your fasting”) — and the Quran does the maths for you: وَأَن تَصُومُوا خَيْرٌ لَّكُمْ, where the أَنْ-clause serves as mubtada. This “re-reading” (الْمَصْدَر الْمُؤَوَّل) is how whole clauses take noun jobs: subject, object, after prepositions.

Each one folds the clause after it into a masdar mu'awwal — an interpreted verbal noun that then takes whatever i'rab the sentence needs. بِمَا نَسُوا reads as بِنِسْيَانِهِمْ. The test is simply whether the clause can be rewritten as a noun.

How do I know a particle is a masdar-maker and not something else?

Try the swap. If the particle and the verb after it can be replaced by a single verbal noun and the sentence still says the same thing, it is a masdar-maker. If the swap breaks the meaning, the particle is doing another job.