Because you're working on TROPOMI/ NO2 data which is in the molecules/cm2 unit and need to convert the molecules/cm2 into microgram/m3, you need to consider the following options:
First, I assumed you were referring to the NO2 vertical column in the stratosphere based on this link (https://developers.google.com/earth-engine/datasets/catalog/COPERNICUS_S5P_NRTI_L3_NO2#bands). The value of this column changes depending on the latitude. Due to gas compression, Colder regions and seasons lead to a thinner stratosphere.
Let assume that its thickness is 30 km (3x10⁶ cm) based in this link (https://sciencing.com/thick-thin-earths-atmosphere-19740.html). So, molecules/cm² are 3x10⁶ molecules/cm³ for a vertical column of 30 km.
Now, you need to consider Avogadro's number (6.02x10²³ molecules/mol), molecular weight of NO2 (46 g/mol), conversion of grams in µg (1 g = 10⁶ µg) and conversion of cm³ in m³ (1 m³ = 10⁶ cm³). Combining all of them (I employed factor method), you got a conversion factor of 2.29x10⁻⁴ for converting values from molecules/cm² to µg/m³ based in these assumptions.
By applying this conversion factor, you can acquire conversions from your original maps using map algebra.
However, you should go over the calculations again to be sure there are no errors in the arithmetic.