Help with time-invariant variable in panel data

Good morning,

I am new here and would greatly appreciate some help. I would like to run a regression in order to see the effect of several variables (GDP, urbanisation rate...) on the production of waste.
I have an unbalanced panel data with 930 observations for 27 EU countries between 1995 and 2017.

In my regression, I would like to include a variable on "environmental awareness" that does not change across time (discrete variable with values ranging from 0 to 5). Nevertheless, running a fixed-effect models results in an omitted variable (as it is time-invariant). My main reason for using a FE model is that the result of my Breusch-Pagan Lagrange multiplier test indicated no significant difference across units (thus indicating that random effects are not appropriate, if I am not mistaken). I am not completely sure of my choice between random and fixed models though.

I am now thinking of using a random-effect mode (which does not omit my variable) l but I would like to know whether I am allowed to do that or whether there is a way I could include my "environmental awareness" variable in the FE model.

All my gratitude goes to whoever takes the time to read this and could help me!